Thank you to all who've responded! Your comments have been very helpful, and I truely appreciate them.
I have decided to keep the name "Elizabeth" for my character because, as Shatnertage wrote, the name spoke to me; and now, the more I write for Elizabeth, the more she becomes her own entity.
I also know that Seven of Nine's biological mother was named was Erin Hansen; but as the show progressed and Seven began to develop her own individuality and eventually emotions, she expressed a certain disappointment and animosity towards her parents for putting her in danger as a child, and for her eventual assimilation. Although Seven willl have learned to forgive her parents for their choices, I don't see her naming her child after them.
I do, however, see her chosing a name which would honor someone or some life-altering event as the case my be. I believe she would be moving past the notion that "designations are irrelevent" to the idea of "designations should have meaning." And of all the individuals close her, Kathryn Janeway would be the most likely person she would wish to honor, as it was Janeway who had liberated her, and who had guided her closely afterwards, followed closely by The Doctor, had the child been a male of course.