An Etymological Dictionary of Family and Christian Names, by William Arthur:
KEMP(E) - In Old English, the term "Kemp" designated a soldier engaged in single combat.
The name Kemp is derived from the Saxon word "To Kemp" or combat, which in Norfolk [County, England] is retained to this day; a foot-ball match being called a camping or kemping; and thus in saxon a Kamper signifies a combatant, a champion, a man-at-arms.
In some parts of Scotland, the striving of reapers in the harvest-fields is still called Kemping." Is this correct or accurate? I don't know. I've also heard stories that a Kempe accompanied William the Conqueror, and therefore the name is of Norman origin.
Marjorie D. Kemp wrote ... the name is Anlgo-Saxon which now means English. But once upon a time these were two germanic races, the Angles and the Saxons (now northern Germany) who were busy invading wherever they could. England, obviously, was a prime invasion target (way, way, back when). KEMP came supposedly from CEMPA which means "ordinary warrior (or foot soldier to us nowadays) or soldier".
Bill Kemp found in The Surnames of Ireland by Edward MacLysaght: KEMP. This English name (Middle-English, kempe, athlete) recurs in Irish records from the fourteenth century till the present day but has never been closely identified with any particular locality. It is now fairly numerous in Dublin and Belfast. See CAMPBELL.... CAMPBELL. Mac Cathmhaoil (battle chief). An Irish sept in Tyrone; in Donegal it is usually of Scottish galloglass origin, viz Mac Ailin a branch of the clan Campbell (whole name is from cambeal, crooked mouth). Many Campbells are more recent Scottish immigrants...
.The name has been abbreviated to Camp and even Kemp in Co. Cavan.