Dametrius \d(a)-met-rius, dam(e)-trius\ as a boy's name is a variant of Demetrius (Greek), and the meaning of Dametrius is "follower of Demeter".
The baby name Dametrius sounds like Dimetrius, Demitrius and Demetris. Other similar baby names are Damarius, Damarios, Dmitrios, Dimitrious, Dimitrios, Demitrios, Demetrio, Demetrice and Demetri.