I’ve often thought about this, but usually come to the conclusion that although I’d like something more unusual, at least my names aren’t the sort that date me. When I was about 10, in 1950, I longed to be called Beryl for some reason. Now I’m glad I’m not. My father wanted to call me Catriona, but wasn’t sure how to pronounce it (CatREEona or CatriOHna) so I wasn’t called that. I’d have liked it, though. My mother liked Alison, but that’s not my name either. I would quite like to be called Caroline - not particularly unusual, but I think it has a nice sound.
I had an unusual surname before I was married. I wish I hadn’t taken my husband’s rather boring name, but it was quite a relief not having to spell it every time I said it!
I don’t like names to be shortened. Susan I like, but not Sue. Elizabeth but not Liz. Some boys’ names, like Christopher, Benjamin and Nicholas, are hardy ever used in full. I think that’s a pity, and it would stop me using them. (Sorry, that’s a bit off topic.)
Some people like a name that stands out, some hate that. My DIL was one of five Katherines in her year at school, which infuriated her, but I have a friend called Felicity who hated being the only one with that name.