What's In a Name
Saruhiko Fushimi is written as 伏見 猿比古 in kanji. 伏見 translates to Fushimi, his family name. 猿比古 is Saruhiko. His name was given to him by his father Niki and the story of it is somewhat insulting.
The start of his name, 猿 is written using the character for monkey. He was given this name because his father thought he looked like a "disgusting monkey" when he was first born. The name was rather unflattering and as he grew up his father often referred to him by it, using it as an insult. When he and Misaki eventually parted ways Misaki began to refer to Fushimi by the same title.
Fushimi's family name is also the title of a ward in the city of Kyoto Fushimi-ku. The name of the ward while written with different characters initially comes from fusu and mizu which translates to hidden or underground water. It is likely the same for our Fushimi. The title is fitting for Saruhiko who is both a hidden weapons user and a member of the blue clan which opposes the red flame.
The last characters that make up Saruhiko's name are 比古 which individually translate to hi which is ratio or proportion and ko which is old or used.