My understanding is that the original Welsh pronunciation rhymed the first syllable with "peg" or "leg".
However, in Australia, where
Megan came to be pronounced "Mee-gan", the pronunciation of
Tegan became "Tee-gan". And that pronunciation spread to North
America when the episodes of the "Dr. Who" television series that featured an Australian woman sidekick of Dr. Who called
Tegan aired.
Even though the show was made in Britain, the Australian pronunciation of
Tegan was used in it. So even though most speakers in the USA pronounce
Megan with the vowel of "peg",
Tegan seems to be usually pronounced with the "ee" sound of "tea".