When Lt. Stamets is in the mycelial network with mirror Stamets and they arrive at Engineering the name plate on the wall behind the mirror Stamets says "USS Stamets". Lt. Stamets said when he was looking around the corridors before reaching Engineering that he recognized it as Discovery. Therefore, the name plate should read "USS Discovery".
One of the pieces of evidence that allows Burnham to deduce that the Lorca she has known is actually the one from the Mirror universe is Terrans' extreme aversion to light. In decades of previous stories involving the Mirror universe, beginning with Mirror, Mirror (1967) and through multiple Mirror-universe episodes of Star Trek: Deep Space Nine (1993) and Star Trek: Enterprise (2001), no such difference in photosensitivity was ever displayed or mentioned.