I know that the English language wasn’t standardized until relatively recently.
But all the other “occupational” names are spelled with the current spelling. Smith, Baker, Carpenter, Barber, Weaver, and so on.
But I’ve never met, or even read about, anyone with the last name “Tailor.” It’s always “Taylor” with a Y.
Why?
I am sure you would have seen Smythe, Bakker, Carpentier and so on. But I grant you that I have never come across Tailor as a last name.
I think you hit it in your first sentence. English wasn’t standardized. “Taylor” was probably the more common spelling at one time.
From what I can tell Taylor and Tailor were both used for the profession with Taylor being more popular. Sometime around the 19th century the spelling of the profession was standardized as Tailor and people who had the last name did not feel the need to change it.
What I want to know is, Y?
Others:
Faulkner from falconer.
Malthus from malt house. (Note the combining into the “th” sound.)
Fry from free.
Foster from forester.
Warner from warriner (rabbit warner dude).
Bailey from bailiff.
Coward from cowherd (or cow-ward).
Hoggart from hogward.
Yates from gates(man).
Webb from web (weaver).
Gardner from gardener.
Languages, and spellings, evolve. Get used to it.
And another:
Clark from clerk
The musician Sting has the family name Sumner. It comes from summoner, a tax collector. Sting has an album called Ten Summoner’s Tales. I suppose that’s a reference to Chaucer work of long ago. Oddly, the album has eleven tracks.
Is Taylor with a “long” A or a “short” A?
*runs away
Webber from weaver
Naylor from nailer
My last name is a thing. It is spelled different from the thing it sounds like. But I still get references of the thing regularly. I don’t think spelling was very standardized early on. No cite, just my WAG.
A few more
Eisenhower from Iron Worker
Wainwright from Wagon Builder
Boatwright from Boat Builder
Hooker from, uh…, Fisherman. Yeah, that’s it!
Or a crochetist.
Eisenhauer (pronounced more or less the same as the US president’s name, but with a German accent :)) makes perfect sense in German (iron cutter, literally), though I don’t think it’s a currently usual word.
Is Tyler “the same name” (with the same meaning) as Taylor? I think it is but not sure.
Or a rugbyist. 
Could this also be from hoh=high and gart/garth=enclosed area/courtyard/greenspace?
A lot of the possible cites may be lost. People thought it was obvious at the time it was created, so they didn’t need to comment.
I think another with a significant-looking spelling difference is Baxter. It’s literally Bake-ster, right?
Cecil has this to say: