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It was common about 100 years ago and has been rather popular again for a while. Thyra and Tyra are pronounced the same way (see Remora's post). It's almost like saying "tear ah" in English, but not exactly.
It's derived from the Norse god Tyr.
I don't like it at all. The reason is that my grandma lost her mother when she was young and then her father re-married a woman who was called Tyra and who was apparently a very bad person.
Sorry I can't tell you more about the name.

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.