Ive never heard of Thessaly or Tessley and I feel like they sound really made up (needs Bromios expert opinion though). Tessa and Theresa are at least real names and I personally like Tessa a lot.
I had a great aunt Ester that went by Tess. Not sure if that's a legit NN for Ester or if she just used it.
Nameberry says: "Thessaly" This name of an area in northern Greece, known in the era of Homer's Odyssey as Aeolus. It's the name of a character in the graphic novel Sandman, and could easily be adopted for a modern little girl.
I like Tessa, and Esther NN Tess is also nice. My MIL's name is Tess and I have never thought anything about it not being a proper first name, so there's that too.
Seeing as how Tessa is my name, I might be bias, but I like it :-) I loved growing up with a name that was easy to pronounce and spell, and I was the only one in my school, which I also loved.
Re: Full name for Tess?
I had a great aunt Ester that went by Tess. Not sure if that's a legit NN for Ester or if she just used it.
Tessa
Esther
Theresa (and its variants)
I know Tess's that are just Tess
Elisabeth
None of the other ones you said
I'll throw a curve ball - Tesni (Tess-nee)
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I like Tessa, and Esther NN Tess is also nice. My MIL's name is Tess and I have never thought anything about it not being a proper first name, so there's that too.
(To me, not too popular is a positive thing!)
Then she can be Tess or Tessie for short.
If you call her Thessaly or Tessley, she will spend her life repeating and/or spelling her name.
ETA: Tessa Claire is very nice