She does not like the name that her husband chose for the baby girl, and she calls her by a different name
Praise be to Allah
Naming the newborn is the right of the father, but it should be done in consultation with the mother, and a name should be chosen that is acceptable to both. But if they disagree, then the father has the right to choose.
Ibn al-Qayyim (may Allah have mercy on him) said: Naming the child is the right of the father, not the mother. This is a matter concerning which there is no difference of opinion among people. If the parents disagree concerning the naming of the child, then it is the father who has the right to choose.
The hadiths quoted above all indicate that. Moreover, the child should be named after his father, not after his mother, so he is called So-and-so son of So-and-so. Allah, may He be exalted, says (interpretation of the meaning): “Call them (adopted sons) by (the names of) their fathers, that is more just with Allah” [al-Ahzaab 33:5].
The child follows his mother with regard to being free or slave, and he follows his father with regard to his lineage and his name; naming defines the lineage. And with regard to religion, he follows the better religion of his parents.
Naming, like education and ‘aqeeqah, falls to the father, not the mother. The Prophet (blessings and peace of Allah be upon him) said: “Last night a son was born to me, and I have named him after my father Ibraaheem.” End quote from Tuhfat al-Mawdood bi Ahkaam al-Mawlood p. 135).
Shaykh Bakr Abu Zayd (may Allah have mercy on him) said, after confirming that:
Based on that, the mother should not dispute or argue.
Consultation between the parents gives a great deal of room for working out a mutually agreeable option in an amicable fashion, thus strengthening the bond between them.
End quote from Tasmiyat al-Mawlood (28-29)
There is nothing wrong with the mother calling her daughter by a different name, so long as the purpose behind that is not to change or show objection to the name the father chose, especially if that is accompanied by urging others to reject the original name. In that case, she is going against her husband, transgressing his rights and offending him.
Our advice to the wife is to fear Allah, may He be exalted, and to accept the name that her husband has chosen, since he has the right to do so from an Islamic point of view, and so long as the name that he has chosen is permissible and is one that is well known and familiar in your environment, and does not include anything that may cause embarrassment or shame to the girl.
And Allah knows best.