I have a cousin named
Tess, just
Tess, people always ask if it's short for something.
I have a dog named
Tessa (we didn't name her, she's not named after my cousin) and we get lots of compliments on her name.
I prefer
Tessa, it just sounds more complete to me. I think
Tessa can stand on it's own. I like both as a nickname for
Theresa.