His name may be a reference to the video game character Mega Man, as the pronunciation of his name as well as his color scheme are similar to Mega Man's.Mugman and Cuphead's animations (when they use the blue potion) may be a reference to when Popeye eats spinach.Just like how Cuphead seems to be based on Mickey Mouse, Mugman seems to be based on Oswald the Lucky Rabbit, sharing a similar color scheme and being the brother of the protagonist.According to an interview with Studio MDHR, the liquid inside Mugman's head is the essence of his soul.
The patch fixes various bugs and addresses prominent gameplay issues, which unfortunately includes doing away with the amusing Mugman Army. The developers at Studio MDHR did some fine-tuning to Cuphead today with Patch v1.1.3.
The red colors are replaced with Pacific Blue color, his straw is shorter & not bendy. Mugman seems very similiar to Cuphead, but however, he has some differences.