I think this is his old school shirt.
(The photo above is from the Hawking press photos, but I wouldn’t put it past him to have worn it more than once.)
“Throughout the conversation, I have been distracted by noticing, every time he leans forward to stub out a cigarette or sip his gin and tonic, the label in his white shirt. It is not a flash designer name, but an old-fashioned Cash-style school tag with “Benedict Cumberbatch” on it in red thread. “Does your mother still sew in your name tags?” I tease as we part company outside the theatre where Hedda Gabler is playing. “Or have you just not bought a shirt in a decade?” Cumberbatch is mortified. “Oh, no. Am I wearing a shirt with a name tag in it? My God, and you noticed. I just hadn’t done any washing for a while, and this seemed clean. Oh, no — now there will be an article in The Sunday Times saying I’m a prat.” That is certainly not the aim.”
(I would link the article but it’s behind the paywall.)
This continues to be precious. He makes reference to this interview in TGG commentary as well.