The photo has since been deleted.
‘Basil’ is thought to be a nod to the Rolling Stones frontman’s late father, who’s first name was Basil.
Mick, 73 and his ballerina girlfriend Melanie Hamrick, 29 welcomes their baby boy – Mick’s eighth child – on December 8.
Sir Mick is also a great-grandfather and has six other children as well as Lizzy and his one week-old son - Karis, Jade, James, Georgia, Gabriel and Lucas - from previous relationships.