Root — English and Irish:
Meaning — 1. English: from Middle English more moor , marsh , fen , area of uncultivated land  (Old English mor), hence a topographic name for someone who lived in such a place or a habitational name from any of the various places named with this word, as for example Moore in Cheshire or More in Shropshire. 2. Irish: Anglicized form of Gaelic Ó Mórdha descendant of Mórdha , a byname meaning great , proud , or stately .

Root — Scottish:
Meaning — patronymic from the personal name Morris.

Root — English and Scottish, Swedish, French and Americanized form:
Meaning — 1. English and Scottish: habitational name from any of the many places called Mor(e)ton, named in Old English as settlement (tun) by or on a marsh or moor (mor) . 2. Swedish: variant of Martin. 3. French: contracted form of Moreton. 4. Americanized form of one or more like-sounding Jewish surnames or of various other non-English names bearing some kind of similarity to it.

Root — English:
Meaning — variants Mosley.  The obvious derivation is from Old English mos peat bog  + leah woodland clearing , but the one in southern Birmingham had as its first element Old English mus mouse , while one in Staffordshire had the genitive case of the Old English byname Moll.  The form Moseley occurs mainly in the West Midlands

Root — English:
Meaning — habitational name from any of the various places with this name, as for example in Cheshire, Lincolnshire, Norfolk, Northamptonshire, Suffolk, and North Yorkshire. For the most part these were named in Old English as Mula s settlement , from the Old English personal name or byname Mula mule  + tun enclosure , settlement , but in some cases they may have been originally farms where mules were reared or kept.