Molmore

Derived from the Gaelic name element máel / mal / maol "tonsured, shorn; (and by extension) disciple, devotee" and the given name More with the intended meaning of "devotee of the Virgin Mary" (since the names of saints were considered too holy for everyday use, they were usually prefixed until the 17th century).
The name was traditionally Anglicized as the etymologically unrelated Myles 1 and Miles.