From mop + -sy.

• IPA: /ˈmɒpsi/

mopsy (plural mopsies)

1. Synonym of moppet.
2. (obsolete) A slatternly, untidy woman.
   • 1936, Anthony Bertram, Like the Phoenix:

     However, terrible as it may seem to the tall maiden sisters of J.P.'s in Queen Anne houses with walled vegetable gardens, this courtesan, strumpet, harlot, whore, punk, fille de joie, street-walker, this trollop, this trull, this baggage, this hussy, this drab, skit, rig, quean, mopsy, demirep, demimondaine, this wanton, this fornicatress, this doxy, this concubine, this frail sister, this poor Queenie--did actually solicit me, did actually say 'coming home to-night, dearie' and my soul was not blasted enough to call a policeman.

From mop + -sy.

1. A nickname for a person with a mop of hair.
2. A given name for a pet animal; stereotypically a shaggy animal looking somewhat like a mop head; frequently a shaggy dog.