Lord above, haven't heard anything about the surrogacy rumours, so assume they are just that rumours.
I'm agreeing about the name with others though. Princess Liillibet, it sounds awfully twee, particularly in a land that would like to promote the whole Disney Princess thing to youngsters, I imagine that moniker is going to feed into the blurred lines of make believe.
The thing about pet "family" names, and I imagine many families have or had them, we certainly did, they grow up around the child, they're a form of endearment sometimes a version of the child's actual name as in "Lillibet" but really whilst they might stick into later years, they're kind of private, often a bit daft and not a moniker anyone would want to stick on a child as their actual name. I think they, Harry and Meghan, over stepped the mark there, I'm not sure they got permission to use Lillibet, I rather thought the late Queen may have assumed they were asking to use Elizabeth. Now the Princess is official, this little girl is saddled with this very Disneyesque label, but the British historical context could well be lost on the wider American society who don't know and may not be interested in our history of kings and queens Something I found out years ago when I was married to a foreign national whilst dragging him around Hever Castle one afternoon and said something along the lines of "you seem bored" to which he replied "English royal families don't interest me" Fair enough that told me!