I'd rather the AI companies make up names, or name their products things like "Clod" than use my name (if they were to ask) - as no matter how good it looks today eventually it'll be some form of laughingstock.
At least GPT is pretty "unique" and they've not polluted search (except for those looking for the GUID Partition Table, RIP).
Any name you pick will immediately override anything that comes before - naming a model Socrates would confuse searches, for example (and it's why I hate the rename of iTunes to "Music" which is a generic term!).