I think
Tess is a lovely name. I would personally use it as a nickname for
Teresa (with this spelling), which is my Aunt's name.
Tess on it's own is a bit insubstantial in my opinion. How about
Tessa? It's a bit longer and more complete than just
Tess, but not as formal as
Teresa. You could use
Tess as a nickname for
Tessa.