From "Ata/Tata" - father. Examples: Mustafa Kemal Atatürk, Tutor, Attaboy; Otats/Otets, but also Tato in plain Macedonian, Tata in Serbo-Croatian. From Proto-Indo-European *tata-, Proto-Italic *tata, etc.
According to this website, http://www.nordicnames.de/wiki/Tatius -- this name has a possible origin from the Greek word 'tatto', which is the Attic form of 'tasso', meaning 'I arrange, I put in order'.