Thaddeus is very nice.
Thaddeus Hugh seems to bring out the snootier parts of the name--both
Thaddeus &
Hugh seem a little snooty on their own, but a lot together. I would go for something a bit rougher, like
Thaddeus Luke,
Thaddeus Lyndon,
Thaddeus Michael,
Thaddeus Anthony, etc. I'm not nuts about
Tad, but I love
Thad. You might also want to consider the Spanish version
Tadeo and the Italian
Taddeo. I love both of these, as well.