Is there a special blessing for entering a new house besides the blessing for the house?

Shalom u'vracha

It is customary to perform a Chanukat HaBayit, a house dedication ceremony according to the Chida:

The ceremony begins by standing at the entrance of the house and reciting the following verses, asking for blessing, protection, and success:

"ברוך אתה בבואך ויהי ה` את יוסף ויהי איש מצליח";
"ויהי דוד לכל דרכיו משכיל וה` עמו";
"ויהי נועם אדני עלינו ומעשה ידינו כוננה עלינו ומעשה ידינו כוננהו";
"אנא בכח גדולת ימינך קבל רינת עמך, שגבנו, טהרנו נורא";

"והנה אנחנו מאלמים אלומים בתוך השדה והנה קמה אלומתי וגם נצבה, והנה תסובינה אלומותיכם ותשתחווינה לאלומתי". 

"Blessed are You when you come in, and may Hashem make Joseph a successful man";
"And David was successful in all his ways, and Hashem was with him";
"May the pleasantness of Hashem be upon us; may You establish the work of our hands; establish the work of our hands";
"Please, in the merit of Your mighty right hand, accept the song of Your people, strengthen us, purify us, O Awesome One";
"And behold, we are sheaves in the field, and behold, my sheaf rose and stood upright, and behold, your sheaves gathered around it and bowed down to my sheaf".

"Barukh ata be-vo’ekha, va-yehi Hashem et Yosef, va-yehi ish matzliaḥ."

"Va-yehi David le-khol derakhav maskil, ve-Hashem imo."

"Va-yehi no‘am Adonai aleinu, u-ma‘aseh yadeinu konenah aleinu; u-ma‘aseh yadeinu konenehu."

"Ana be-ko’aḥ gedulat yeminakha, kabel rinat amekha; sagveinu, taheirenu, nora."

"Ve-hineh anachnu me‘almim alumim be-tokh ha-sadeh; ve-hineh kamah alumati ve-gam nitzavah, ve-hineh tesovenah alumoteikhem va-tishtachavena le-alumati." 

Continue with a specific request for mercy, success, and the blessing of the house:
"May it be Your will, Hashem our God and God of our ancestors, Merciful and Compassionate King, that You should have mercy upon us, and in the merit of the ancient names that come from these verses, may You grant success to us and to all our descendants in this house, both in general and in particular, and may we all be successful and blessed in everything we do, and may You save us from the evil eye, from all sin, from all sickness, and from every trouble, and may our homes in every place be full of good, successful, and blessed for us and for our descendants. Amen, may it be Your will."

"יהי רצון מלפניך ה` אלוהינו ואלהי אבותינו, מלך רחום וחנון שתתמצא רחמים עלינו, ורוב רחמיך ובזכות שמות הקדומים היוצאים מפסוקים אלו, תצליחנו לנו ולכל זרעינו בבית זה בכלל ובפרט, ונהיה כולנו מוצלחים ומבורכים בכל מכל כל, ותצילנו מעין הרע, ומכל חטא, ומכל חולי, ומכל צרה, ויהיו בתינו בכל מקום בתים מלאים כל טוב, מוצלחים ומבורכים לנו ולזרענו, אמן כן יהי רצון."

"Yehi ratzon milfanekha, Adonai Eloheinu ve-Elohei avoteinu, Melekh raḥum ve-ḥanun, she-timtza raḥamim aleinu, u-rov raḥamekha, u-ve-zekhuyot shemot ha-kedumim ha-yotzim mi-pesukim elu, tatzliḥenu lanu u-le-khol zare‘einu ba-bayit zeh bi-khlal u-vi-ferat;
ve-nihyeh kulanu mutzlachim u-mevurakhim bekhol mikol kol;
ve-tatzilenu me-‘ayin hara, u-mikol ḥet, u-mikol ḥoli, u-mikol tzarah;
ve-yihyu bateinu be-khol makom batim mele’im kol tuv, mutzlachim u-mevurakhim lanu u-le-zar‘einu.

Amen, ken yehi ratzon."  

Also recite the following verses:
"May Your kindness, Hashem, be upon us as we have hoped in You";
"Show us, Hashem, Your kindness and grant us Your salvation";
"And I trusted in Your kindness; my heart will rejoice in Your salvation; I will sing to Hashem because He has dealt bountifully with me";
"Behold, God is my salvation; I will trust and not be afraid, for my strength and song is Hashem, and He has become my salvation".

"יהי חסדך ה` עלינו כאשר יחלנו לך";
"הראנו ה` חסדך וישעך תתן לנו";
"ואני בחסדך בטחתי יגל לבי בישועתך אשירה לה` כי גמל עלי";
"הנה אל ישועתי אבטח ולא אפחד, כי עוזי וזמרת יה ה` ויהי לי לישועה".

"Yehi ḥasdekha Adonai aleinu ka’asher yiḥalnu lakh."

"Hare’einu Adonai ḥasdekha, ve-yeshakha titen lanu."

"Va-ani be-ḥasdekha bataḥti; yagel libi bi-yeshu‘atekha.
Ashirah la-Adonai ki gamal alai."

"Hineh El yeshu‘ati; evtach velo efḥad,
ki ‘ozi ve-zimrat Yah Adonai, va-yehi li li-yeshu‘ah."

If a mezuzah has not been affixed at the entrance of the house until the house dedication, one should affix a mezuzah, secure it with a nail, and recite:
"Blessed are You, Hashem our God, King of the Universe, who sanctified us with His commandments and commanded us to affix a mezuzah".

"ברוך אתה אדני אלוהינו מלך העולם אשר קדשנו במצוותיו וצוונו לקבוע מזוזה".

"Barukh ata Adonai Eloheinu Melekh ha’olam, asher kideshanu be-mitzvotav ve-tzivanu likboa mezuzah."

  
Some have the custom to recite the Shehechiyanu blessing for the new house, (and some have the custom to eat a new fruit or wear new clothing at that time, so that the Shehechiyanu blessing applies both to the fruit or clothing and to the new house):
"Blessed are You, Hashem our God, King of the Universe, who has granted us life, sustained us, and brought us to this time".

"ברוך אתה אדני אלוהינו מלך העולם שהחיינו וקיימנו והגיענו לזמן הזה".

"Barukh ata Adonai Eloheinu Melekh ha’olam, sheheḥeyanu ve-kiyemanu ve-higi‘anu la-zeman ha-zeh."

Lastly, it is customary to give charity or to commit to do so in the future.

Learning for the house dedication:
After the ceremony, it is customary to study sources for blessing the success of the way and the blessing that the Torah should dwell in the house. Any text can be studied, and it is common to study Mishnas from Masechet Berachot, Masechet Beitzah, and Masechet Tamid.

In conclusion, it is customary to read from the Zohar, Part 3, page 50a, from the Gemara in Masechet Baba Metzia, page 107a, and from the Rambam, Mishneh Torah, Laws of Personal Development, Chapter 5, Halacha 11:
"It is the way of wise individuals for a person to first establish a livelihood for himself, and afterward buy a home, and afterward marry a wife...."
Also, one reads from the Rambam in the Laws of the Chosen House, Chapter 1: "It is a positive commandment to make a house for Hashem...."

We conclude this request with:
"May it be Your will, Hashem our God and God of our ancestors, God of Abraham, God of Isaac, and God of Jacob, Merciful and Compassionate Father of Mercy, that the learning we have learned from Your holy Torah be considered a pleasant aroma before You. And may Your abundant mercy rest upon the owner of this house - [So-and-so, son of So-and-so and So-and-so], who, with the beginning of his dwelling in this house, desired greatly and makes his first efforts - this house dedication with the words of Your holy Torah to establish the house and dedicate it with the words of Torah. Therefore, in the merit of Your holy Torah may You bless this owner of the house who has endeavored in this learning, him and all his household with blessings forever. And may this house be successful and blessed in all of its endeavors. And may there be in this house the sound of joy and happiness, tranquility, and security; joy and happiness may be found in it, and all sorrow and sighing may flee away. Please, by the strength of Your abundant mercy, be with them as a shelter, a protection, and a refuge.

And may You annul from us all harsh and evil decrees, and through the authority of the Supreme King, may You distance from this house every harmful thing, every fear, and every fright. By the power of the holy names from these verses, let no one stand before You; may Your fear and dread be placed by Hashem your God upon the face of all the earth upon which you shall tread, as He has spoken to you.

And may the supplies stated in this verse protect and save from all evil for this owner of the house and all his household, and may You grant them success in all their endeavors. And may You save them from all evil. May they be fat and flourishing. Merciful and Compassionate, Guarding, Supporting, Saving, and Redeeming, in the abundance of Your mercy, accept our pleas and respond to our requests, for You hear the prayers of all mouths; act for the sake of Your name, act for the sake of Your right hand, act for the sake of Your Torah, act for the sake of Your holiness."

"יהי רצון מלפניך ה` אלוהינו ואלוהי אבותינו, אלוהי אברהם ואלוהי יצחק ואלוהי יעקב, אל רחום וחנון אב הרחמים, שיהא חשוב ומרוצה לפניך הלימוד שלמדנו בתורתך הקדושה כריח ניחוח. וברוב רחמיך המרובים תרחם על בעל הבית - [פלוני בן פלוני ופלונית] הזה, אשר בתחילת בואו לשכון בבית הזה, אוותה נפשו ויעשה תחילה וראש, חנוכת הבית הזה בדברי תורתך הקדושה, לייסד את הבית ולחנכו בדברי תורה. ובכן בזכות תורתך הקדושה תברך את בעל הבית הזה אשר השתדל בלמוד זה, לו ולכל בני ביתו ברכות לעד. ויהיה להם הבית הזה מוצלח ומבורך בכל מכל כל. וישמע בבית זה קול ששון ושמחה, השקט ובטח, ששון ושמחה ימצא בה, ונסו יגון ואנחה. אנא בכוח רוב רחמיך היה עליהם סתרה, צנה וסוחרה.

ותבטל מעלינו כל גזרות קשות ורעות, ובהורמנא דמלכא עלאה, מני שים טעם להרחיק מן הבית הזה כל מזיק וכל פחד וכל בהלה, בכוח שמות הקדושים היוצאים מפסוקים לא יתייצב איש בפניכם, פחדכם ומוראכם ייתן ה` אלוהיכם על פני כל הארץ אשר תדרכו בה כאשר דבר לכם.

וע"ב אתון אשר בפסוק זה, ישמרו ויצלו מכל רע לבעל הבית הזה ולכל בני ביתו, ויצליחם בכל מעשה ידיהם. ותצילם מכל רע. דשנים ורעננים יהיו. רחום חנון שומר תומך מציל ישר פודה, ברוב רחמיך תקבל תחינתנו ותענה עתירתנו, כי אתה שומע תפילת כל פה, עשה למען שמך, עשה למען ימינך, עשה למען תורתך, עשה למען קדושתך."

"Yehi ratzon milfanekha, Adonai Eloheinu ve-Elohei avoteinu,
Elohei Avraham ve-Elohei Yitzḥak ve-Elohei Ya‘akov,
El raḥum ve-ḥanun, Av ha-raḥamim,
she-yehe ḥashuv u-merutzeh lefanekha ha-limud she-lamadnu be-Toratekha ha-kedoshah
ke-re’aḥ niḥoaḥ.

U-ve-rov raḥamekha ha-merubim terachem al ba‘al ha-bayit — [peloni ben peloni u-pelonit] — ha-zeh,
asher be-tḥilat bo’o la-shkon ba-bayit ha-zeh, avta nafsho
ve-ya‘aseh teḥillah ve-rosh ḥanukkat ha-bayit ha-zeh
bi-divrei Toratekha ha-kedoshah,
le-yesed et ha-bayit u-le-ḥankho bi-divrei Torah.

U-ve-khen, be-zekhut Toratekha ha-kedoshah,
tevarekh et ba‘al ha-bayit ha-zeh asher hishtadel be-limmud zeh,
lo u-le-khol benei veto berakhot la-ad.
Ve-yiheyeh lahem ha-bayit ha-zeh mutslaḥ u-mevorakh bekhol mikol kol.

Ve-yishama‘ ba-bayit zeh kol sason ve-simḥah,
ha-sheket u-vetaḥ,
sason ve-simḥah yimmatzeh bah,
ve-nasu yagon va-anacha.

Ana be-ko’aḥ rov raḥamekha,
heyeh aleihem seterah, tzinnah u-soḥerah.

U-tevatel me-‘aleinu kol gezerot kashot ve-ra‘ot,
u-ve-hurmanah de-Malka ‘ila’ah,
mini sim ta‘am le-harḥiq min ha-bayit ha-zeh kol mazik ve-kol paḥad ve-kol behalah,
be-ko’aḥ shemot ha-kedoshim ha-yotzim mi-pesukim: lo yityatzev ish lifneikhem;
paḥadkhem u-mora’akhem yiten Adonai Eloheikhem ‘al penei kol ha-aretz asher tidreku bah
ka’asher diber lakhem.

Ve-‘A"b etun asher ba-pasuk zeh,
yishmeru ve-yatzilu mi-kol ra‘
le-ba‘al ha-bayit ha-zeh u-le-khol benei veto,
ve-yatzliḥem bekhol ma‘aseh yedeihem.
Ve-tatzilem mi-kol ra‘.
Deshenim u-re‘ananim yihyu.

Raḥum, ḥanun, shomer, tomekh, matzil, yeshar, podeh —
be-rov raḥamekha tekabel taḥinateinu ve-ta‘aneh atirateinu,
ki atta shome‘a tefillat kol peh.

‘Aseh le-ma‘an shemekha,
‘aseh le-ma‘an yeminakha,
‘aseh le-ma‘an Toratekha,
‘aseh le-ma‘an kedushatekha."

With blessings - Binyamin Shmueli