I think it depends on the name.
If a girl is named Brittney, Heather, Lacey or other names unfairly associated with lower intelligence and bigger boobs, that may become a defining part of her ID. If she is smart, she is constantly defying societal expectations of her name. If she is unattractive, she's not living up to the expectation of her name... etc.
If someone is named Meatloaf, Jaguar, Kaymeryn (Pronounced "Cameron"), Anakin (sorry, Star Wars fans!) or anything else odd or out of the ordinary, I think that's going to influence their experience on this Earth quite a bit, at least socially speaking. This will not change personality per se, but it will alter the development of that individual. Their name automatically makes them different, unique, odd, an outsider... etc.
Names are a tricky thing. It's horribly unfair that some parents seem to be using their child's name as a platform for their own creativity. If you're going to name your boy Nathaniel, please spell it the traditional way, rather than Naythanyel (I'm not making this crap up!). Other cringeworthy examples: Breighanna, Izabellah, Mykal, Zakkary, Jaxxson.......
If parents stopped and imagined THEMSELVES with such names, I think the trend would taper off significantly.
Honestly, people should name themselves. Seriously. I know it's not feasible, but damn! That would be so much more fair.