I believe this is a reference to the novel "I am a Cat" (吾輩は猫である, Wagahai wa neko dearu) by author Natsume Souseki. It's opening sentences are the following:
which, translated into English, is:
I am a cat. I don't yet have a name.
The reference is more apparent if we compare the two in Japanese. The grammatical structure of the sentences is very similar:
吾輩は 女装男 である。名前は 桂木
I am a cat:
吾輩は 猫 である。名前は まだ無い。
All the words other than the nouns are the same. The use of 吾輩 (wagahai) for "I", である (dearu) as a sentence-ending phrase would both be strange in modern writing. In addition, the general structure of the two sentences are similar enough that this is almost certainly not a coincidence.
The novel is very popular in Japan, being Natsume's first major literary work and one of his top three most read (the other two are Kokoro and Botchan), and Natsume himself being in all likelihood the most important writer in Japanese history. It would not be strange at all for it to be referenced here.