How such clothes would be termed in the rag trade -make, label, house - and how Joe Public talks about such clothing are two different things:
What is the make of the T-shirt?
If it was from K-Mart or such - but at that end of the market, you'd just say, "I got it - you can get/buy it -at K-Mart. or Where did you get your T-shirt?
What is the label of the T-shirt?
If it was from Tommy Hilfigger or Calvin Klein. Again, while they are referred to as designer-label clothes, one just says, "It's Calvin Klein" or "It's a Tommy Hilfigger."
What is the house of the T-shirt?
Do Dior and Chanel and the like deign to make T-shirts? Anyone acquiring such fashions would merely say, "It's from Dior" or "It's a Chanel."
If your friend had asked me that question, I would have replied, "What sort do you want?" or if it was another of the same type he already had, "Where did you get it from?" He then says, from K-Mart, Marks and Spencers, Next, RiverCity, Timberland, Top Man.
"Who makes them? (meaning Klein, Hilfigger or whomsoever).
I have not been in the position of being asked to pop into Chanel for an item. lol