Praise be to Allah.
This womans desire to take an Islamic name and to change her family name from that of her former husband is quite correct, but it is not permissible for her to call herself after anyone except her legitimate father no matter what the reasons for wishing to do so. Allaah says (interpretation of the meaning): "Call them (adopted sons) by the names of their fathers" [al-Ahzaab 33:5].
The Prophet (peace and blessings of Allaah be upon him) said: "Whoever calls himself by other than his fathers name (or attributes himself to someone other than his father), will be cursed by Allaah, the angels and all the people." (Reported by Ibn Maajah, 2599; see also Saheeh al-Jaami, 6104).
And Allaah is the Source of help.