I say TEE-gun, and I can't say I like it. It sounds trendy and harsh, I don't see much of a feminine side at all, even though I know it is a legit female name and all.
I'd pair it with something pretty, strong, and feminine.
Tegan KatherineTegan JudithTegan MiriamTegan HelenaTegan Teresa (I rather like the alliteration)
Tegan CassandraTegan AdelleTegan JuliaTegan RuthTegan FionaTegan VioletTegan GeorginaTegan RachelTegan RebeccaTegan UrsulaTegan JaneTegan LouiseTegan GabrielleTegan ChristinaTegan Charlotte
Like any?