If the name on the account is not a name that was ever your legal name, it is not likely that a name change will be possible. Names can be changed on an account in the following circumstances:
A legal name change
A minor misspelling
And in the case of an account for a registered business, a change in the designated contact for the company.
Changing from a fictitious name (or, as in your case, a name unrelated to your legal name) to a legally recognized name is not something that is supported. If the account is not currently limited, you may wish to close the account and open an account using the correct information.
Advice is voluntary. Kudos / Solution appreciated.