The first three adult books were great, as were the first five kids/young adult books. After that the author settled into a formatted writing that just turned me off. I read them back in the 70's and they were EXTREMELY popular. It's no biggie being named after a character, there are plenty of other places the name Sharra could come from.
Be greatful that you weren't named after the Beauty and the Beast show, I know of SO many orange cats who were named Vincent from that, and kids, no matter who their parents are, are often named after tv characters.
The fact that the name is not related to Pern alone is a good thing - just ignore the Dragonrider series and live your own life. Nobody would guess the name was a reference to someone in a book.