If Amaterasu is the Sun, then Tsukuyomi is the Moon. Tsukuyomi's full name is Tsukuyomi no Mikoto.
Tsukuyomi is taken from the word Tsuku (月) which means Moon (or it can also be read as the month of the year such as January, February, and so on). In the modern era, the word Tsuku was changed to Tsuki, which also still means Moon.
There are several versions of his last name, the first possible being taken from the word Yomi (読み) which means to count or to read. Later versions say that his name is read Tsukuyumi, which means Moon Bow.