Is there an English word for "a name you legally gave yourself"?

Solution 1:

If the person writes under a "false name" then pseudonym is the answer.

If the person has chosen to call him or herself with one name only, such as Adele, Prince, Pelé or Sting, then the term is mononym. For example, “Her mononym is Shakira.”

A single name by which a person, thing etc is known. For example, Madonna (the pop musical artist)

Talking of Prince, when he changed his name to the so-called ‘love’ symbol , for a number of years he was known as "The Artist Formerly Known as Prince", "TAFKAP", or just "The Artist". Likewise anyone could rename him or herself and say:

I'm [new first name], formerly known as [old first name].
OR
I'm [new first name], but I used to be called [old first name].

If a person dislikes their first name (for whatever reason), they can just call themselves with a different name. Sometimes a family nickname sticks, and that person grows up with that name. Changing a name by deed poll might include a lengthy process depending on one's nationality.

The most common use is a name change through a deed of change of name (often referred to simply as a deed poll). Deeds poll are used for this purpose in countries including the United Kingdom, Ireland, New Zealand, Hong Kong and Singapore. In the UK, a deed poll can also be used to change a child's name, as long as everyone with parental responsibility for the child consents to it and the child does not object to it. The child's parents execute the deed poll on the child's behalf. In some other jurisdictions, a person may simply start using a new name without any formal legal process.

Wikipedia

Oxford Dictionaries:

pseudonym
(noun)
a fictitious name, especially one used by an author.
"I wrote under the pseudonym of Evelyn Hervey"

synonyms: pen name, assumed name, alias, professional name, sobriquet, stage name, nickname

Solution 2:

Alias is the name that you use in addition to your real name. It doesn't have a connotation of self-given, but it doesn't have a connotation of others-given, either.

an additional name that a person (such as a criminal) sometimes uses.

[Merriam-Webster]

"Self-given alias" will be much clearer in your context.

Solution 3:

Consider, moniker.

: a name, title or alias Computer Desktop Encyclopedia

He gave himself the moniker of Drew Danburry, hit the road with his guitar and never looked back Kuer

Everyone knew her as Nancy.

Dear Word Detective: I have often been puzzled by the derivation of the word "Monica" or "Moniker" when used in the context "Can you please stick your moniker on here," meaning "can you please sign this" or "can you please put your signature on here." In the past I have been told that it was possibly used in a kind of coded slang used by Irish Americans. But even if that were true, it still doesn't explain the derivation. I would have thought it much more likely to be cockney rhyming slang -- I'd love to bet there was a famous socialite called Monica Rignature or something ("Rignature - Signature"). Ha Ha! -- Adam Archer.

Well, that's not absolutely impossible, since a couple of the theories that are considered possible explanations for "moniker" (as it is usually spelled) are nearly as odd. That's a sort of backhanded way of admitting that no one knows exactly where "moniker," meaning "a name, especially an assumed one," or "a nickname," came from, but at least we have some entertaining possibilities to poke at.

"Moniker" first appeared as slang around 1851 in several different spellings, including "monaker," "monarch," "monekur," "monikey," "monnick," and "monniker." By the 20th century, the spelling "moniker" seems to have largely won out, although the variant "monica" is cited in the Oxford English Dictionary from 1968.

The pioneering etymologist Eric Partridge favored the notion that "moniker" is related to "monarch," in the sense of "king," in that one's name "partly rules" one's life. Frankly, this seems a bit of a stretch to me (and rather literary for what was, after all, originally street slang).

Another interesting theory explains "moniker" as originating in "back-slang" (a reverse slang common in Britain) for "ekename." "Ekename" was the original form of our modern word "nickname," "eke" being an old English word meaning "additional." (Through a process called "metanalysis," the "n" in "an" in the phrase "an ekename" drifted over and gave us "a nickname." The same process transformed "a napron" into "an apron.")

Anyway, the reverse slang for "ekename" would be "emaneke," which gradually mutated, according to this theory, to "moneker" and so on. Again, this is far from impossible, but seems a bit too elaborate.

Perhaps the simplest theory (and I like simple theories) is that "moniker" is just a blending, perhaps originally jocular, of "monogram" and "signature." The Word Detective