I was silently horrified when my son and his wife used my second name, ( and my mother's first name) as a middle name for their daughter . I think it was a kind gesture but it's a name I just can't stand. My mother, who had become very vocal with dementia, would have told them right out that it's a bloody awful name and what were they thinking. She died before the baby was born so we managed to avoid an outburst.
Someone mentioned upthread that there will be a few more Lilibets being born and that's very true. Happens a lot these days. However there were only 2 Lilibets born between 1900 and 1988 in England and Wales. People would have been aware of the nickname but didn't copy it.