From the mid-fifteenth to the mid-eighteenth centuries the occupation of "tailor" seems to have been spelled "taylor", often with a capital T.
Before that time there is record of "tailor"or "taillour" following the Norman French taillour, (modern French tailleur).
Before mid-fifteenth century
1297 R. Gloucester's Chron. (Rolls) 6391 A robe he let him ssape
uerst of blod red scarlet þere Þe ssarpe stones bi þe stret is tailors
were..Þe tailors corue so moni peces uor is robe ne ssolde powȝe.
c1412 T. Hoccleve De Regimine Principum 472 The taillours..moot
heer-after soone Shape in þe feeld.
1466 in Manners & Househ. Expenses Eng. (1841) 354 Herry Galle
taylour,..axsethe for makenge of a longe gowne of pewke, ij.s.
1530 J. Palsgrave Lesclarcissement 68 A tayllours wyfe or a woman
1600 W. Shakespeare Henry IV, Pt. 2 iii. ii. 149 Shal. What trade
art thou Feeble? Feeble A womans tailer sir... Fal... but if he had
bin a mans tailer hee'd a prickt you.
c1600 Wriothesley's Chron. Eng. (1875) I. 5 This yeare the Taylors
sued to the Kinge to be called Marchant taylors.
1611 B. Rich Honestie of Age (1844) 34 I doe see the wisedome of
women to be still ouer~reached by Taylers, that can euery day induce
them to as many new fangled fashions as they please to inuent.
a1616 W. Shakespeare King John (1623) iv. ii. 196 I saw a
Smith..With open mouth swallowing a Taylors newes.
1663 S. Pepys Diary 25 May (1971) IV. 155 Into the coach again;
and taking up my wife's Taylor.
1704 J. Pitts True Acct. Mohammetans iii. 16 They all sit down
cross-legg'd, as Taylors do.
1751 S. Johnson Rambler No. 123. ⁋5 I..sent for my taylor; ordered
a suit..and..staid at home till it was made.
Surnames were introduced intermittently in England from the time of the Norman Conquest (1066). However there is evidence that many were still being created in te fifteenth century.
Perhaps, and it is only speculation, the name "Taylor" may date from a time when the occupation of that name had adopted the "English" spelling of "taylor".
All examples from the Oxford English Dictionary.