She does not like the name that her husband chose for the baby girl, and she calls her by a different name

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.