On Tuesday, the billionaire Tesla CEO replied to one of his Twitter followers to reveal that Grimes was in labour.
When asked to reveal the name of his son, Musk tweeted: “X Æ A-12 Musk.”
It is not clear if Musk was being serious about the name, or if he was being cryptic or joking.
The unusual name has prompted many to question how it is pronounced, with one Twitter user suggesting: “X Ash Archangel.”
The user’s tweet explaining the origins of the name was liked by Musk, implying it could be correct.
The tweet suggests the name’s origins could have something to do with the Scandinavian alphabet, in which Æ is pronounced “ash”.
A-12 is thought to be a reference to the Lockheed A-12, a CIA aircraft codenamed Archangel.
Grimes first hinted she was pregnant in January with an Instagram picture that showed her posing naked, with a digitally-superimposed image of a foetus visible through her translucent stomach.