Where did the name of all time loser 'billy muggins'...

[janzman]

...originate..

[Mamyalynne]

http://www.worldwidewords.org/qa/qa-mug1.htm

[Mamyalynne]

Various foolish characters named Muggins have appeared over the years, mostly since the latter half of the eighteenth century. There doesn’t appear to be a single prototype on which the others are based.

The earliest cite of Muggins in the OED is:

1705 P. A. Motteux Amorous Miser ii. i. 19 They are a couple of close-fisted old Muggins.

There’s also a single extant citation of muglard, meaning “miser” from 1440. This is perhaps related to the Old French musgode, or “treasury.” Muggins may originally have appeared as “miser,” and widened into a term of general approbation, but that’s rather speculative.