Very good R J and let us not forget that surnames perse, or at least surnames passed down the generations via the male line, were not a "thing" until the poll tax of 1377, at which time they became mandatory.
Nobility had surnames of a sort, but even those can't be used to trace patrynomy. For instance the surname Lacy is derivative of de Laci, a Norman appellation that designated the origin of the lineage,which could be a place in Normandy , or the de could designate the first fiefdom in Angleland.
It often happened that such lines went extinct in the male line, or an up and coming scion of another minor nobility married into a more prosperous or pompous line and adopted the name as his own, such as happened to, for example, the de Laci's,
Yet ths "nobles" ostensibly of Norman ancestry, but not necessarily, would name there children as (ex;) William FitzJohn), Fitz is an anglo contraction of fils de or "son of"
Commoners, per se, did not have surnames, but were known by their occupation, (copper, potter, smith)place of residence(hill, forest, whidby,York, dale-a valley, physical characteristic (tall, short, whitehead) or patronymic (ex: son of David, or Davis, Davidson, Davidsson, depending on region Welsh, Scotch, Saxon, Norse or Dane in which the first of the name lived).
By the way, any town or name which ends in "by" is of Norse origin. For instance Gouldsby was Goulds farmstead. And these farmsteads became vills and towns
Personally I abhor the term illegitimate,as it has an unsavory and derogatory cultural connotation, for me non paternal event is sufficient, and NPE's can be from many different events other than intercourse outside the blessings of a religion or state.
Slaves in America were not allowed to marry, so they would have practices like "jump the broom". In frontier communities and especially immigrant communities, where a religious authority was not available,a couple could unite in a handfast ceremony.
As an aside, "illegitimacy" was more prevalent amongst royalty and nobility than we are informed. Stability of succession was important, for stability of the realm or estate.
Lacking knowledge of sperm and ovaries, these people believed that in the ejaculate was a "mini human" a homonculus.
Males of the era enaged in many activities that had an adverse effect on sperm carrying the Y chromosone, or were simply away from the castle too often,or some other cause, to play their role in reproduction.
As a consequence, certain ministers of court, would even promote a liaison with the Queen, just to ensure stability in the realm by succession.
Such a cause might be the reason that YDNA testing of Richard III revealed a different Y haplogroup than other descendants of Edward III.
It is questionable if any of the descendants of Edward III are actually his descendants. It is thought by some that Edward III was homosexual and possibly did not father any children.
At least his wife Isabella of France, took up with Roger Mortimer, had Edward III's purported lover, Piers Gaveston, executed, along with Hugh Despenser elder and younger. (all of the above are also my purported ancestors, including Edward III).
Henry VIII had difficulty producing a male heir, and most certainly for that reason his court went out of their way to introduce healthy young females into his presence, and when they failed to produce a male heir, it is my opinion that they manufactured or exposed infidelity as a means of getting rid of her and introducing another. There must have been succession panic in the court, as Henry was getting on in the years,and suffered at least one debillitating infirmity from his youth.
Had they not failed, this country (and us) would not exist, and the continent would be Spanish/French.