Let them fight to decide it! Whoever wins, keeps her name. Since you want to make one change. >:) As for Angela and Lilith being opposites on purpose, Caleb and Lilith Vatore are also opposites on purpose. In the story I am writing, Caleb and Lilith Vatore are older than the game hints that they are, and in my backstory, Lilith Vatore was originally christened Elizabeth, and called Lilly by friends and family.
When Caleb (who wasn't going to live to 30, his heart had been damaged by his childhood battle with the rheumatic fever, but they didn't know that...) was turned, his sister Lilly, who had been taking care of him and running the estate with their inheritance, confronted Melissa (Miss Hell) and found out just enough to lead her to Vlad, and she went pounding at his door, fearlessly demanding he turn her. He was so impressed with her determination and her reasons (so that she would be equal in power to Miss Hell and therefore able to protect Caleb from her, should she return to attempt to command him) that he did it, partly because he knew Miss Hell had been his first mistake.
Lilly then took the name Lilith, which suited her excellently, as she had been born to a world in which she could not even sign documents but had to bring them to her brother's bedside even though she was actually running everything, and her choice of name reflected her rejection of patriarchy.
Despite being himself a product of patriarchy from 300 years prior, Vlad embraced Lilith's fiery personality and felt he couldn't have chosen better this time, for progeny.
So that's my story, and that's why Lilith Vatore's name is important to her.