The singer captioned the video shared to her Instagram Story with a love heart as X Æ A-12 curled into a tight little ball and his dad patted his back lovingly.
In the days since the baby's birth, the internet has been obsessed with trying to figure out how his name is pronounced.
And the duo has offered up even more confusion as their pronunciations of the name appear to be different.
In an interview on The Joe Rogan Experience, Musk, 48, discussed the name, seemingly claiming it was pronounced "X Ash Archangel Twelve".
"First of all, my partner's the one that actually mostly came up with the name," he explained. "It's just 'X,' the letter 'X,' and the 'Æ' is pronounced 'ash' and then 'A-12' is my contribution. Archangel 12, the precursor to the SR-71, coolest plane ever."
In an Instagram post from Thursday, May 6, however, the 32-year-old musician offered a different take.
A fan commented on her photo – a pair of pictures from her photoshoot with Italian Vogue – asking, "how do you pronounce the baby's name?"
Grimes, whose real name is Claire Boucher, replied to the comment.
"It's just X, like the letter X," she wrote. "Then A.I. Like how you said the letter A then I."
Different still was Grimes' previously offered explanation of the meaning of X Æ A-12's name.
"X, the unknown variable," the singer wrote, adding an emoji of two crossing swords. "Æ, my elven spelling of Ai (love &/or Artificial intelligence).
"A-12 = precursor to SR-17 (our favourite aircraft). No weapons, no defences, just speed. Great in battle, but nonviolent," she continued, adding a white heart emoji. "(A=Archangel, my favourite song) (metal rat)."
Musk later commented, correcting the aeroplane his girlfriend referenced.
"SR-71, but yes," he wrote.
