While “Amun” probably does mean “the hidden one,” I believe that the term was usually understood as a reference to the Amun, the god whose cult at Karnak and Luxor came to dominate much of Egyptian religion during the New Kingdom.
Tutankhamen means “the living [ankk] image [tut] of Amen” (“Amen,” “Amun,” and “Amon” being variant transliterations of the same god’s name). Of course, you could also translate that as “the living image of the hidden one,” but there’s no doubt that it meant the god Amen as The Hidden One.
Remember, Tutankhamen’s name was originally Tutankhaten, a reference to the god “Aten” who Akhenaten (possibly Tut’s father) had established as the only god of Egypt during the Amarna period. After Akhenaten’s death, all references to Aten (a heretical belief in the eyes of most traditional Egyptians) were effaced–literally, in the case of stone inscriptions, and symbolically, in the case of Tut’s name. The god Amen was restored in Aten’s place in both Tut’s name and in Egyptian society in general.