This is a very confusing sentence. 次の日、ロシア人にロシア語を習いに来たとき、下の我々の部屋に暁梅が来た。＝When (someone) came to learn Russian language to a Russian person next day, 暁梅 came to our room which was in downstairs. 本人は自分の名前を小梅だと書く。＝She writes her own name as 小梅. 1.Was it the Chinese person 暁梅 who came to study Russian? The subject is missing in this sentence, so we do not know who is studying Russian from this sentence. 2.Did he (or she?) come to the room below after the Russian lesson or was the Russian lesson taking place in下の我々の部屋? The Russian lesson was held upstairs and our room (我々の部屋) was in downstairs. Besides, the sentence says "When", so we do not know if s/he came before or after the lesson. 3.I am completely baffled by the use of を after自分の名前, I can’t find the corresponding verb. The main sentence is "本人は書く" ＝S/he(subject) writes(verb). What does she writes? ⇒ name.＝ "名前を（object）". So, s/he writes name. What sort of name? ⇒his or her own ＝”自分の”. So, s/he writes his/her own name. How does s/he write? ⇒小梅＝”小梅だと”. So, "s/he writes his/her own name as 小梅" is the whole sentence. 4.本人は自分の名前を小梅だと書く And finally, does it mean that the name of the person is小梅 and not暁梅? I assume that the person's real name is 暁梅, but s/he writes her own name as "小梅". Hope it helps you to understand.

Is this the original paragraph you're reading? http://homepage2.nifty.com/pekingdo/rireki.htm From this context the sentence can be translated like: "When 暁梅 came (to the dorm) to learn Russian from Russian person, she(暁梅) visited our(the author and 同室のオッサン) room downstairs.She writes her name as 小梅. " 暁梅 is a Chinese girl the author met at 頤和園. The pronunciation of 暁梅 and 小梅 are the same in Chinese, as 雲小泉-san mentioned. Why does she write her name differently? I don't know.

次の日、ロシア人にロシア語を習いに来たとき、下の我々の部屋に暁梅が来た。本人は自分の名前を小梅だと書く。 There is no Russian lesson mentioned here at all. The next day, when we came to Russia to learn Russian, 暁梅 came to our room. He writes his own name 小梅. 暁梅 looks like a Chinese name to me. He rewrites it as 小梅 to make it look like a Japanese name. The pronunciations are exaclty the same. That's my take anyway.