There's no canon answer for this, so I will give a subjective answer in the spirit of canon.
I don't see Harry as telling Albus Severus about his namesake for the first time at King's Cross. I think he was reiterating what he had already told Al probably multiple times. Anyone who has kids knows that they tend to ask repetitive questions, even at eleven, and they express their worries by seeking repeated reassurance (ad nauseum sometimes). The movies are not canon, but if you examine the inflection in Harry's voice as he talks to Al at King's Cross, it's clear they've had the discussion before, and that Harry is reassuring Al about Slytherin and using Al's namesake to drive the point home.
Regarding Slytherin, J.K. Rowling has stated that Slytherin became more diluted and was "not the pureblood bastion that it once was." There were more Muggleborn Slytherins than ever before by the time Albus Severus went to Hogwarts. However, Slytherin's dark reputation persisted, although it wasn't as hardcore as it was during Harry's era, thus Al's resistance to being Sorted to Slytherin. Harry clearly tried to work with Al about Slytherin fear and prejudice while he was talking to Al at King's Cross. I would posit a guess they probably had the Slytherin conversation before as well.