Whatever the distant origin of mooch, the verb *mycan and its cognates have been part of European slang for at least two millennia. [Liberman]
Related: Mooched; mooching. As a noun meaning "a moocher," from 1914.
The basic sense in place names is 'marsh', a kind of low-lying wetland possibly regarded as less fertile than mersc 'marsh.' The development of the senses 'dry heathland, barren upland' is not fully accounted for but may be due to the idea of infertility. [Cambridge Dictionary of English Place-Names]