… although, I guess any pronunciation will be wrong because the actual name was “Πτολεμαίος”, so if you wanted a correct transliteration you would have to use “Ptolemaious”

Regardless, Joey is still closer to the correct pronunciation.

The "right" pronunciation depends on what you take for reference. If you're treating the word as an English one, the woman is right - English doesn't allow this sort of initial cluster, and spelling-wise it's well-established that some initial consonants are mute (see e.g. "knife").

And, if treating the word as a Koine Greek one... odds are both are butchering the word so much that [pə] wouldn't save the day. Even the man is likely pronouncing it as [pə.'tɒl.ə.mi]; the Greek word would be more like [pto.le.'mɛ:.os], or [pto.le.'maɪ̯.os] with a really conservative pronunciation.

I'd take [gb] and [pt] all day over [ŋθ] or [θɹ].

Unless you mean [g͡b] (the co-articulated consonant, often common in languages from West Africa). Then I'm saying noooope.