I have at least five onomastic dictionaries here that give the origin of Murgatroyd as 'Margaret's clearing'. The earliest recorded form is Mergretrode (1379) so the Moor Gate hypothesis is obviously wrong. Also, the earliest forms if Ingham are Ingeham (1086), Ingheham (1115) and Ingaham (1163) so it was either the homestead/village of somebody named Inga or, as suggested in Mills' Oxford Dictionary of Place Names (2003) "a word meaning 'the Inguione', a member of the ancient Germanic tribe called the Inguiones". No one has proposed that it has anything to do with the common -ing suffix in Birmingham, etc. which originally meant 'people of, dwellers at'.