No one is quite certain of the exact origin of tango's name. Tango is a Latin-American genre of music and dance which combines European and African elements. Specifically, it is a combination of milonga, candombe, and habanero, with influences of Spanish flamenco. This multi-cultural background makes definitively identifying its etymology difficult.
One leading theory is that the name tango derived from tamgu, which in the Niger-Congo language of Ibibio means "to dance." Considering that many of the slaves in the Spanish empire came from this region, this is a plausible explanation.
Another theory is that it is named after tambor, the Spanish word for drum. Slaves pronounced this word as tambó giving it an onomatopoeia-like quality. However, drums are not a significant part of modern tango music, so this explanation may not be legitimate.
Some linguists claim that tango may have Latin origins. It may be derived from the Latin word tanguere meaning "to touch." Indeed, Tango is characterized by close contact between dancers.
Some believe that tango's name refers to a place where African slaves would gather to sing and dance. Several West African languages refer to slave merchants and their markets as tangomao. In Brazil, this was often used to refer to slave traders and slave markets. It is possible that tango originated from this name and came to signify any place in which slaves would gather. It then may have come to be associated with their music and dance itself.