When my name was called, my heart started pounding.
Literal
Name [object-を] called [and], chest [subject-が] thumped-thumped.
どきどき is a heartbeat mimetic — onomatopoeic for the pounding or fluttering of a nervous/excited heart. どきどきする is the standard collocation for 'to be nervous/excited.' 胸がどきどきする makes the body-part explicit. One of the most recognizable Japanese mimetics.