Is there a word for "under one's real name?"

As far as I know, there is no word specific for this, because it's publishing something under an alias that's the exception to the rule. It's normal that people will publish under their own name, so it's only the exception that gets special attention.

However, a generic way of saying this could be self-identified:

Three years after releasing his last album as Fakename Jones, John Smith released his first self-identified album Tuesday.

Note that this could be open to misinterpretation, making it seem as if it's the album identifying itself rather than the singer. However, the context should make it clear what's actually meant.

Three years after releasing his last album as Fakename Jones, John Smith released his first album signed by his real name.

Or

Three years after releasing his last album as Fakename Jones, John Smith released his first album under his real name.