Author's note: for the overview post on gods and goddesses of the ancient Maya, go here
Only found in the Madrid Codex, God Q was -- as mentioned in the overview post on the ancient Maya gods and goddesses -- once classified as part of God F. Thompson was the first to officially talk about reclassifying God F into three gods, giving them new designations -- the other two of which are God R and God A'.
As to his name, it could be that God Q's was called Lahun P'el. The glyphs the ancient Maya used for his name include the number 10.
God Q's costume tends to include the death eyes and death collar -- like God A --, as well as a knotted headband (theorized to be paper or cloth.)
Another notable feature of God Q is what is called his "facial band" in The Major Gods of Ancient Yucatan, Issue 32 by Karl A. Taube. This band may be made of lines of dots, bands or just lines, and goes from his forehead, through an eye and stops at the far side of his cheek. Theories exist as to the nature of this band. One theory states it refers to human skin while another says it relates to stone.
God Q is commonly understood to be either a god of death, human
sacrifice and/or war. This god is also thought to be a god who lived in Xibalbá, and is often drawn alongside Kisin (God A) in the Madrid Codex.
On three pages of the Madrid Codex, God Q is fighting Ek Chuah (God M), a god of merchants.
Missouri State University: MAYA GODS AND GODDESSES
"Star Gods of the Ancient Maya: Astronomy in Art, Folklore, and Calendars"; Susan Milbrath; 2000
"Native American Mathematics"; Michael P. Closs; 1996
"The Major Gods of Ancient Yucatan, Issue 32"; Karl A. Taube; 1992