Ok but what if it's like this...
Davos tells Gendry to keep his name to himself, right? He says "the king has a lot in his mind" so we the viewers are left to assume that Davos has filled Gendry in on the details of what's going on.
So Gendry knows that the new King in the North is Arya's brother.
Arya, the girl he loves. The person who has had the most impact in his life. The only person he has truly ever trusted. The only family he ever could have had.
She was already above him. A high-born girl and a bastard boy. Only now he's not just any bastard boy. He's got noble blood. Royal blood. Baratheon blood. His father and her father fought together.
But she's still a princess. And he's still a bastard.
But if he can just impress this king.
If he can fight with him. Prove himself.
He could be legitimized. He could be granted his father's ancestral home. No other Baratheons have a claim to Storms End. It could be his. He could become a lord in his own right. Someone worthy of marriage to the youngest sister of the king. Arya has no claim to Winterfell. But maybe, just maybe, he could give her Storms End.
"I've been getting ready. Never knew what for, but I've always known I'd know it when it comes."
He's been waiting for his chance.
And now he’d going to take it.
TL;DR Gendry hasn't mentioned Arya yet because he needs to prove himself to Jon first, to prove that he's worthy of loving his sister.
