it depends on what you mean by unique. if they're real names or real variants on names, that's fine; honestly people will side-eye characters in rp for the most ridiculous reasons, just ignore them. but if it's a really weird respelling of an existing name or something you just made up, i'd... question the point of that, you know? there are tons of real names that aren't commonly used in rp.
some ic reasons you can use for your character having an unusual name: - they (or their parents, or grandparents) are not american, - they were named after a relative, - their parents were dead-set on a certain name for a certain gender, and when they were surprised by their baby being the opposite gender they decided to stick with it anyway, or feminize/masculin...ize it, - the character themselves picked up a nickname (especially a really weird/pretentious one) as a teenager, or an online handle, or whatever, and it just stuck, - they are named after a mythological figure, fictional character or famous person, - they were named after the state or city they were conceive/born in, - their name was misspelled on their birth certificate and they never got it changed, - their parents decided to combine two names, - their parents are hippies, - their parents are actually super pretentious yuppies who gave them a really obnoxious name like maddyzin, - their parents decided on a double first name,