Doctor Marigold is the titular "cheap-jack" in Dickens' Doctor Marigold. Is "Marigold" his real name, with "Doctor" an addition, or is "Doctor Marigold" a nickname?
His given name is "Doctor Marigold"
The manner of how Marigold got his name is explained in the first two paragraphs:
I am a Cheap Jack, and my own father’s name was Willum Marigold. It was in his lifetime supposed by some that his name was William, but my own father always consistently said, No, it was Willum. On which point I content myself with looking at the argument this way: If a man is not allowed to know his own name in a free country, how much is he allowed to know in a land of slavery? As to looking at the argument through the medium of the Register, Willum Marigold come into the world before Registers come up much,—and went out of it too. They wouldn’t have been greatly in his line neither, if they had chanced to come up before him.
I was born on the Queen’s highway, but it was the King’s at that time. A doctor was fetched to my own mother by my own father, when it took place on a common; and in consequence of his being a very kind gentleman, and accepting no fee but a tea-tray, I was named Doctor, out of gratitude and compliment to him. There you have me. Doctor Marigold.
"Doctor" is his given (first) name. "Marigold" is his family (last) name. The explanation for "Doctor" is referred to later, when Marigold relates his interactions with the gentleman from the Deaf and Dumb Establishment in London:
We saw the gentleman four times in all, and when he took down my name and asked how in the world it ever chanced to be Doctor, it come out that he was own nephew by the sister’s side, if you’ll believe me, to the very Doctor that I was called after.
And here again, he emphasizes that he is not an actual doctor:
The most difficult explanation I had ever had with her [Sophy] was, how I come to be called Doctor, and yet was no Doctor.
He is sure of how his name came to be and asserts in the first paragraph that a man should be allowed to "know his own name". A scan of the text gives me no reason to suspect anything other than Marigold's explanation of his own name. It might not be a normal kind of name, but then Marigold isn't a normal kind of person.
All quotes are [sic] and bolding is mine