For the record, I don't actually believe these rumors, not at this stage - I think the sites are just desperate for clicks.
Replacing Kate just because RR left is too stupid, I find it hard to swallow that they would be that dumb, and still try to pass the show off as Batwoman.
They could make a whole new show with a whole new character of course, that's fine, and name it after whatever that character's mantle is.