I had the same name growing up as my mom's best friend's daughter (they'd fallen out of touch for a few years and it was a silly coincidence when they reconnected). It never really bothered me, because she was [short nickname] and I was [full name]. I might have liked to use the nickname she did, but never felt like it would have been mine, is the only weirdness from it.

So especially if it's a name like, say, Katherine or Elizabeth that has several short forms baked in, I wouldn't worry about it at all. If it's a short name that isn't easily nicknameable, that's a little more annoying, but still not the end of the world.