The word Hibah refers to a gift that is not in return for something and has no strings attached. Giving this name to a baby girl as an acknowledgement of Allaah's blessings and in gratitude to Him for His favour is something praiseworthy. 

This name has an origin in the Book of Allaah, and from it are taken the names Wahb and Mawhoob.  

Al-Zamakhshari said in his commentary on the verse (interpretation of the meaning), “My Lord! Grant me (offspring) from the righteous” [al-Saaffaat 37:100]:

i.e., give me one of the righteous, meaning a child, because the word hibah usually refers to children although it is also used to refer to a brother in the verse (interpretation of the meaning): “And We granted him [wahabna lahu] his brother Haroon (Aaron), (also) a Prophet, out of Our Mercy” [Maryam 19:53]. And Allaah says (interpretation of the meaning): “And We bestowed upon him [wahabna lahu] Ishaaq (Isaac) and Ya’qoob (Jacob)” [al-An’aam 6:84] and “and We bestowed upon him Yahya (John)” [al-Anbiya’ 21:90]. ‘Ali ibn Abi Taalib said to Ibn ‘Abbaas (may Allaah be pleased with them), when he congratulated him on the birth of his son ‘Ali Abu’l-Amlaak: May you gave thanks to the Bestower (al-Waahib) and may you be blessed in what was given (al-mawhoob). Hence the child may be given the name Hibat-Allaah [gift of Allaah], Mawhoob, Wahb and Moohab. End quote. 

Al-Kashshaaf, 4/54, 55 

As for the various spellings that people give this name, such as Hibah [with ta’ marbootah] and Hiba [ending with alif], and so on [not to mention the various spellings in Latin script – Translator] this does not mean that the meaning varies according to the various spellings; rather it is various mistakes that people make, but they all go back to the verb wahaba, the noun of which is hibah, with ta’ marbootah, the ‘t’ sound of which is silent. As for the other spellings in Arabic and so on, these are mistakes for which we cannot find any particular meanings in Arabic language dictionaries, or they are kinds of diminutives and affectionate nicknames, which may be pronounced differently or take different forms, according to the accent of those who use these names. 

It says in al-Mu’jam al-Waseet (2/1059):

… Hibah refers to a gift that is given without anything in exchange. In shar’i terms it means allowing a person to take possession of an item without anything in return. End quote. 

See also the answer to question number 69950. You may also refer to a number of questions on our site that have to do with the naming of children, such as question number 101401. 

And Allaah knows best.