Trish is one of the characters from the Devil May Cry series of games. She started out working for the bad guy but switched sides in the first game and ended up as the main character's partner. Given that the series has a thing for making references to the Divine Comedy, odds are that in this case the name was intended as a derivitive of Beatrice.
Too minimalist, girly, and nickname-y. I can't easily imagine this as the official name of a woman past the age of 30. It makes me think of trashy and annoying British women, actually. It's sad if you get called ''trash'' for having this name, as it's not exactly your own choice to have a crappy name.
I knew a Trish and it wasn't a nickname but her full first name. Poor kid. The bullies called her "Trash" and there was no escape for her because she had no options. Please consider giving your daughter more to work with as one finds in the name Patricia, or at least Trisha. It's only fair! You can still call her Trish at home if you want to, but at school, she'll have a choice and may chose Pattie or Shaw. Well, anything's better than Trash!