The Phethean surname, along with Vivian, Fython, Fithyan,Fiddian,Phythien Phythian etc is derived form the French Vivian, Vivien and Latin Vivianus; a derivative of vivus ("Living"), the name of a 5th -century martyr not uncommon in England from the 12th century. Its pronunciation and spelling are difficult and it appears in a variety of forms. There is much dialectical replacement of "f" and "v" cf Fivian and Fithian; also replacement of "th" and "d" cf Fidian. The initial "Ph" is probably just an artefact of transcription.

In addition "Surnames" (E. Weekley; John Murray 1917) states

"Frithu, peace, has given us many favourite font-names which have later become surnames, e.g. Domfrith (Dunsphrey, Dunpress), Frithugar (Fricker), Frithumund (Fiddyment) . To the last name, or to some other compound of Frithu, such as the once favourite Frithuswith or Friswid, patron saint of the University of Oxford, belong Fiddy, Fiddian, Phethean, Phythian. This element often becomes Free in modern surnames, e.g. Freestone from Frithustan, Freelove from Frithulaf It also appears via Old French in Frizzle, Froysell, which in Scotland has unaccountably become Frazer— and in Fr. Froissart, represented by our Frusharad, Frusher".

Bardsley, Charles Wareing. A Dictionary of English and Welsh Surnames With Special American Instances. Baltimore, MD, USA: Genealogical Publishing, 1967. Originally published London, 1901, quotes the following references to the surname:

Phythian, Phethean. —Bapt. the son of Fithion,’ i.e. Vivian. when passing through Bolton, Lanc., on Sept. 27 i886, I saw ‘John Phethean, plumber and gas. fitter,’ over a window in a street leading to Haliwell.

Henry Fithion, co, Kent, 1273. A.

Richard Fithion, co. Kent, ibid.
Hugh Fifiane, co. Soms., i Edw. ITtr:. Kirby s Quest, p. 122.

Robertus Fethethyan, 1379: P.T. Yorks. p. 262.

Hugh Phytheon, of Tetton) 1582: wills at Chester, i. 6s.s

John Fitheon, of Overton, 1613: ibid.p. 151

Richard Phytheon of Moston, 1593:,wills at Chester, i. 151

In the 6th Hen. VIII (1514—5),"WilIiam Byrthels, son and heir of Fithian (or Vivian) Byrtheles,” grants to trustees all his messuages,' &c. : East Cheshire, ii. 357.1624. Married—Thomas Fytheone and Jane Smith: Reg. Prestbury, co. Ches., p. 246.

One individual had his surname spelled John Fiffeon, Phiffiion, Pfiffian, Phithian and Fitheon between 1604 and 1638; another in 1712-1734 as Thomas Phydian, Fython, Phythian and Pitheon.` The information I have obtained from Cheshire illustrates the local variation in spelling in just one county. It is noticeable how there are clusters of particular spellings in various localities.