Edward is a traditionally Anglo-Saxon name that only came back into vogue as a name for English royalty because Henry III was a big fan of Edward the Confessor. I'm not sure Richard would be giving his kids Anglo-Saxon names like Edward or Edmund (I don't what inspired Henry III to name his second son that...).
A cursory search throws up numerous theories for how the name Lionel came about as a name for the Duke of Clarence either because Edward III was a fan of the character Sir Lionel in the Arthurian mythos or because the coat of arms Hainalt (Lionel of Antwerp's mother's family) was lions or because his father was 'the Lion of England' (making Lionel, a 'little lion'). None of these would apply for Richard.
Sweeping through the previous generations of the Norman family, there's obviously Robert (though if William Clito is still around and causing trouble Richard mightn't want to name his heir after Clito's father; though Richard could name him in honour of his half-brother Gloucester), a
Mauger, a
Geoffrey and a
Hugh/Hugues. There's also Godfrey, from Adeliza's family, which was suggested as a name for Richard himself upthread.
As for Eleanor of Aquitaine- William X might live longer or have a son (hell Eleanor
herself could be born male ITTL).
If she does still become Duchess of Aquitaine in her right then the French royal family will still try to snatch her up (and this will facilitated if she's under age when she succeeds and her father still names the King as her guardian). Worth noting that French royal dynamics could be radically different ITTL- Louis VII's elder brother
Philip might live and ascend the throne.
