TeVelde explains further:

"The Horus name of a successor of Peribsen is Khasekhem (the power has appeared). It has been suggested that Khasekhem is identical with Khasekhemui (the two powers have appeared). If that is indeed the case, 2) then we should have a development reminiscent of Sekhemib taking the Seth name Peribsen. Over the serekh in which Khasekhemui is written, however, the Seth-animal does not appear alone, but in company with the Horus falcon. The name Khasekhemui is sometimes supplemented htp nbwy imyw.f (the two lords who are in him, are reconciled). Thus both Peribsen's Seth name and Khasekhemui's Horus-Seth name proclaim the reconciliation of Horus and Seth."

(the two lords who are in him, are reconciled.)

Here is that door jamb in its entirety:

From _Hierakonpolis_, Part 1, by J. E. Quibell, B.A., With Notes by W. M. F. P.

There is more evidence of Khasekhemy's name in granite, however this evidence is in fragments. Nekhen News, Volume 11, 1999 of Hierakonpolix.org tells about them, discovered in 1935. However, they weren't published back then, possibly because it's impossible to reconstruct the whole object. Fortunately, enough pieces can be assembled to show his name:

"Probably the most important of our fragments measures a mere 27x22cm. It bears the name of Khasekhemwy, “The Two Lords are at peace with him.” The name is inscribed in the frame of the royal serekh, a formalized element of palace architecture surmounted by a Horus falcon and the Seth animal facing each other, a motif unique to this king."

Furthermore, Petrie in _Royal Tombs II_ shows Khasekhemwy's seal impressions that were found in Umm el-Qaab, tomb V. Unfortunately, this book isn't at Etana yet, so I depend on the image capture made by "FRAF":

Meanwhile, here is another of Khasekhemwy's seal impressions:

Period - Dynasty 2 (2686BCE-2890BCE)
Found at - Abydos, height 5 cms length 8 cms width cms diameter cms
Petrie Museum UC36854