Recent use of the phrase in African American English
The expression has been in use among African Americans for at least 28 years. Geneva Smitherman, Black Talk: Words and Phrases from the Hood to the Amen Corner (1994) offers this definition of the term:
CALL SOMEBODY OUTA THEY NAME To insult someone; to talk about a person in a negative way, especially to call the person a name or to hurl an accusation at the person. "She come talkin bout I stole her ring. I don't appreciate nobody callin me outa my name" (i.e., implying that she's a thief).
A Google Books search finds a number of matches for "called me outa [or outta] my name." From Derek Bell, And We Are Not Saved: The Elusive Quest For Racial Justice (1987):
"All that progress, as you call it, didn't keep that white redneck cop from calling me outta my name and pointin' his gun at you when you try to help."
"Well, Delia, that could have happened to anyone interfering like I did."
From Living Blues, issues 76–83 (1988) [snippet]:
Women talks about me and lies on me, calls me outta my name.
They talks about me, lie about me, calls me outta my name.
All their men come to see me just the same.
From Gayl Jones, The Healing (1998):
So some guy noticed your complexion ain't flawless, so what? Guys always telling me about my flaws. I remember the first man that called me outa my name called me Possum, on account of I usedta didn't say nothing to nobody about nothing, and especially men.
The phrase appears in various other Google Books texts, as recently as Jazz Jordan, Lust & Hip Hop 3 (The Ms. Mogul Series) (2015):
"You're one crazy bitch. You know that? I gave you everything and then some, and you're gonna play me like this?"
Shontay cut her eyes at him. “I can't believe you had the nerve to call me out of my name. I am the mother of your child! Don't you have any respect for me at all? This is one of the reasons why I can't be with you anymore. Besides, I've met somebody else, and I'm in love with another man."
Eighteenth-century use of the phrase in England
I was very surprised to find instances of "call me out of my name" from the 1700s, though these may or may not be direct ancestors of the term now used in African American slang. From Henry Fielding, Joseph Andrews (1742):
'...Was ever such a pitiful dog, to take up with such a mean trollop? If she had been a gentlewoman, like myself, it had been some excuse ; but a beggarly, saucy, dirty, servant-maid! Get out of my house, you wh——e!' to which she [Mrs. Tow-wouse] added another name, which we do not care to stain our paper with : it was a monosyllable beginning with b——, and indeed was the same, as if she had pronounced the words, she-dog ; which term we shall, to avoid offence, use on this occasion, though indeed both the mistress and maid uttered the above-mentioned b——, a word extremely disgustful to females of the lower sort. Betty [the servant] had borne all hitherto with patience, and had uttered only lamentations ; but the last appellation stung her to the quick. 'I am a woman as well as yourself,' she roared out, 'and no she-dog; and if I have been a little naughty, I am not the first; if I have been no better than I should be,' cries she, sobbing, 'that's no reason you should call me out of my name : my be-betters are wo-orse than me.'
From The Batchelor: Or Speculations of Jeoffrey Wagstaffe, Esq. (1769):
I was beginning to grow serious upon this subject, when I received the following letter. My much valued correspondent, however, calls me out of my name, by styling my Speculations the HUMOURIST, as I have have for some time dropped that title, on the very just reasons, and do, for the future, intend to appear under that of my real character, the BATCHELOR, which I have this day assumed.
"Brother Jeoffrey," says she [Letty Love-youth] , "you know I have always kept up a good character with the world, and , thank God, my reputation has always been spotless ; besides, I hope I have behaved towards you as towards you as a tender, affectionate sister ; ('tis true I am many years younger than you) and that I should live to be taunted by that young Gipsy to be called out of my name ; in short, to be abused by the scandalous title of Old Maid, is what I cannot bear."
From Dr. Last in His Chariot [a translation of Moliere's Maladie Imaginaire] (1792):
Dr. Last. My own chariot's below.
Ailwou'd. A cart, a wheelbarrow, for such scoundrels.
Dr. Last. Don't call me out of my name.
Ailwou'd. I can't sirrah.
Dr. Last. You did, you did, and I'll make you pay for it.
Ailwou'd. Get out of my house.
The instances from the 1700s are astonishingly similar to and consistent with the examples that occur in the 1980s and later, though I can't say with any certainty that the later instances represent a direct survival or revival of the older phrase. But if the modern phrase isn't a survival or revival of the older one, it is certainly the product of a striking coincidence in wording and usage.