As a
Finn, I can't say much about perceptions of
Thyra or
Tyra in Sweden (expect that both of these names seem to be dated among the Swedish speaking Finns, their popularity peaking in 1900-1919). However, here are good examples how to pronounce
Thyra and
Tyra:
https://fi.forvo.com/search/thyra/sv/ and
https://fi.forvo.com/search/tyra/sv/ . The pronunciation of the letter Y is quite different in Scandinavian (and Finnish) languages compared to other languages, so it's quite tricky explain how to pronounce it to foreigners. I hope that hearing these names said aloud gives a better idea how they're pronounced.