It didn't mention his portrait at the end of the book, and I wondered if that were because he was imposed on the school by the Ministry of Magic, and it was the school's way of not recognizing him as such. But Harry did remind his son, before he went off to Hogwarts, that he was named after two of the school's Headmasters.
Some serious anthropomorphizing here--I think the castle itself, as a fortress of deep magic, accepted Snape as Headmaster. A lot of Snape's memories in "The Prince's Tale" take place in the castle and Hogwarts grounds. It's like the castle knew.
But, there wasn't a picture of Dumbledore in the office when he was the current Headmaster. And after Snape died, there wouldn't have been time for a new one to show up.