What does Theodosia mean, popularity, numerology and more. The name Theodosia is of Greek origin. The meaning of Theodosia is G-d's gift. It is also of Latin origin, where its meaning is gift of G-d.ess than 5 boys were given the name. View the Theodosia Name Popularity Page to see how the popularity trend for Theodosia has changed since 1880, or to compare the popularity of Theodosia to other names. Theodosia has the diminutive (nickname) Dosia.