IIRC the giant strong bad head says "my doge" in his second appearance in email 150 (alternate universe), rather than in email 94. hrwiki is down (surprise surprise) so I can't check.
The guy who has been very in the whole "what if the us government stops processing payments" thing said official government guidance is that it's pronounced doggy
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Dog, E. Doge. DOGGY.
Yes this is a .gif/.gif situation, yes this is a stupid hill to die on!