From Charlotte M. Yonge's book History Of Christian Names, published in 1863,
pages 2-3:

"The invention of original names usually takes place in the early stages of a people's history, for a preference soon arises for established names, already borne by kindred, and as the spoken tongue drifts away from the primitive form, the proper name becomes a mere appellative, with the original meaning forgotten, and often with a new one incorrectly applied to it."

And so, Farthegn became Ferthing.  Actually, there was a tendency to write the personal name like this very early.  Before the year 1000 it was spelled Fertheng on a document, and Ferthen, Farthen, Farthin and Fartheng on coins, very similar to how the modern surname is spelled. The spelling ferthing is no longer used in the English langauge. Interestingly enough, however, the word "ferthing" means traveling in Norwegian, not "a fourth of". The Danish word for the number four is fire (pronounced "FEE-rer") and the two words are obviously unrelated. The Swedish coin, the ferding, was always spelled with a d and never with a th. So, etymologically, it was much easier to make the transition from Farthegn to Ferthing than it was to make the transition from feorthung to ferthing. And it made the transition much sooner, too, for by the time the surname Ferthing appeared, the coin and the measurement were still being called the "ferlyng", "ferdyng", "ferting", and "fardel", never "ferthing". Only after Farthegn was changed to Ferthing did the coin and the measurement slowly become known as the ferthing.

"The ear catches the word imperfectly, the lips pronounce it after their own fashion, and the first writer who hears it, sets it down to the best of his ability, to be read, as it may chance, by others, ignorant of the sound the letters were meant to represent, and thus striking out absolute novelties." 

From P. H. Reaney's The Origin of English Surnames,
page 126:

"The post-Conquest clerks, who were largely of French birth or training, showed a marked tendency to give personal-names the continental spelling and pronunciation with which they were familiar, often giving a man's name in more than one form, but modern survivals prove that many of these forms were in actual use."

For example, in 1086 the post-Conquest clerk spelled Robert Farthegn's name Fardenc,  literally translated Farthing. It is also unusual that a name that is supposed to have multiple origins should have only one modern spelling.  A fourth of a parcel of land was not only called a "ferthing," but a "ferling," a "ferding," and a "ferting." In Somersetshire it was usually known as a "ferling", while it was commonly referred to as a "fardel" in Glastonbury. And in the late 1300's, when most Englishmen already had surnames, the ferthing coin was always known as the "ferlyng" in London.  Why are there no modern surnames with these spellings?  And for that matter, why is there just one spelling that covers all three origins? The answer may be found in Jan Jonsjo's Studies on Middle English Nicknames, and Gillis Kristensson's Studies on Middle English Topographical Terms. Evidently, neither one of these Scandinavian authors felt that the term ferthing had a lasting influence on the formation of nicknames or topographical surnames. In his book The Story of Surnames, L. G. Pine comments on the fact that most nicknames disappeared before they had a chance to become inherited surnames, page 92:

"The number of nicknames is considerable, though it is unwise to assume that names which look like nicknames are really such."...and..."Their disappearance proves that the nickname origin of surnames is rightly relegated to the last place in the history of the subject."

Again, neither the coin or parcel of land were spelled "ferthing" during the time period in which surnames were formed. Sir Henry Ellis tells us that, of all the references to "a fourth of" in Domesday Book, the spelling "ferthing" is never used. The unit of land measurement was called a "ferling" and a "ferding". A quarter of a penny was called either a "ferding", "ferdinc", "ferting", or "quadrans", (General Introduction to Domesday Book, by Sir Henry Ellis, 1833, pages 156-157, 169). The spelling "ferthing" can only be found as a surname during this period.

Mr. Reaney's The Origin of English Surnames, page 121:

"The Scandinavians, unlike the Anglo-Saxons and the continental Germans, had a habit of using the same personal-name in different generations and branches of the same family.  It was a common practice, too, for a man to name his son after some notable chief or a particular friend.  'The departure of the Scandinavian peoples from common Germanic custom is at this point so marked,' notes Sir Frank Stenton, 'that it requires some special explanation.  In the opinion of most scholars, it is connected with the late survival in the north of the belief that the soul of an individual was represented or symbolized by his name, and that the bestowal of a name was a means of calling up the spirit of the man who had borne it into the spirit of the child to whom it was given.' "

In his Family Names and their Story, S. Baring-Gould writes eloquently on the bestowal of personal names on children, pages 49 and 53:

"But with the name it was otherwise, and by imposing that of a heroic ancestor on a child the child became his reincarnation, and acquired all his qualities as surely as if that ancestor had been distilled into its feeding-bottle."
"The practice of reproducing a favourite name in a family lasted for many generations after the idea of reincarnation had been abandoned. The father's or grandfather's name was given to the child out of affection to the former possessor, and perhaps for no other reason; but it continued to be given."
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