English: from a Norman personal name, Filimor, composed of the Germanic elements filu ‘very’ + mari, meri ‘famous’.

                                                F I N N
Irish: reduced Anglicized form of Gaelic 'O Finn 'decendant of Fionn', a byname mening 'whit' or 'fair-haired'.  This name is borne by several families in the west of Ireland.
English: from the Old Norse personal name Finnr 'Finn', used both as a byname and as a short form of various compound names with this first element.
German: ethnic name for someone from Finland.

                                            F I S C H E R
German, Danish, and Jewish (Ashkenazic): occupational name for a fisherman, from Fisch + the agent suffix -er.  This name is widespread throughout central and eastern Europe.

                                            F L E M I N G
Locality.  A native or inhabitant of Flanders.
See Flanders.
Locality.  A name given to a native of Flanders, a County or Earldom of the Low Countries, or Netherlands.  It took its name either from Flandrina, the wife of Liderick II., Prince of Buc, or Flambert, nephew of Clodion, King of France.

                                                        F O R K E R

​​Scottish: variant of Farquhar. German: variant of Volker.

                                                      F A R Q U H A R

Scottish (Aberdeenshire): reduced Anglicized form of Gaelic Mac Fhearchair ‘son of Fearchar’, a personal name composed of the elements fear ‘man’ + car ‘loving’, ‘beloved’.

                                                            F O S T E R

English: reduced form of Forster. English: nickname from Middle English foster ‘foster parent’ (Old English fostre, a derivative of fostrian ‘to nourish or rear’). Jewish: probably an Americanized form of one or more like-sounding Jewish surnames, such as Forster.

                                              F R E E M A N
One who enjoys liberty, or is entitled to a franchise, or peculiar privlage, as the freemen of a city or state.

                                                           F U L L E R

English: occupational name for a dresser of cloth, Old English fullere (from Latin fullo, with the addition of the English agent suffix). The Middle English successor of this word had also been reinforced by Old French fouleor, foleur, of similar origin. The work of the fuller was to scour and thicken the raw cloth by beating and trampling it in water. This surname is found mostly in southeast England and East Anglia. See also Tucker and Walker. In a few cases the name may be of German origin with the same form and meaning as 1 (from Latin fullare). Americanized version of French Fournier.

 Anatomy  of  the  " F " Surnames

Origin - Meanings of Surnames beginning with " F "

McBride - Bumpus Genealogy