This is only a story because Harry and Meghan made it a story at the time by assuring everyone they had the Queen’s blessing. If they’d stayed silent, which is often the best PR move, then it wouldn’t be a big thing.
They can, of course, call their child whatever they like. However, if this was a thread on AIBU (We’ve chosen my elderly grandmother’s personal pet nickname, used only my her deceased husband and parents, as our baby name and she is upset. AIBU) and then there was a massive drip feed about a family falling out, I expect the OP would get roundly roasted for being a dick.
If people took off their ‘I hate the royals’ goggles and looked at it as falling out between any average family then it does look shitty on the part of Harry and Meghan. If they put an elderly lady in that position then no wonder she was upset.