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.)