I was very happy to see in recent updates that more names have been added to the available selections, but I feel that it does not have nearly enough choices.
It might be time to consider reworking the way names are chosen. Either by greatly expanding the names available and partitioning them alphabetically in separate lists or, by finally just integrating the text filter into name selections.
For a year now I have desperately wanted to rename my main wizard's winged catastrophe pet in honor of my real-life cat that passed away, but Figaro isn't an available name.
I'm sure there are lots of other people in similar situations.