Mog rhymes with log: Merriam-Webster gives “MAWG,” and many British speakers say it with a short o, like “mog” in “moggy.” As in Clem Ziroli, King of Mogging.
Wiktionary lists /mɒɡ/ for British English and /mɔɡ/ or /mɑɡ/ for American English. Mogging is “MAWG-ing.”