Question about selling stocks I was gifted when I was a minor.

I just found out I was gifted a handful of stocks as a minor, and now that I'm an adult I'd like to sell some of them. My hang-up on doing so is that one of my parent's names is on the stocks alongside my own (I assume because I was a minor when they were purchased). Would selling them as-is bring any taxes upon them, or do I need to have their name fully removed from the stocks to avoid that?

I'd like to sell some of them as soon as possible, but want to be sure any taxes fall onto only myself before I do so.