The 3rd-century Roman soldier saint often illustrated slaying a dragon is George, commonly called Saint George.
According to Christian tradition, George served in the Roman army and was executed during the persecution associated with Emperor Diocletian, traditionally in AD 303. He is linked with Lydda in Palestine and is venerated as a major military saint in both Eastern and Western Christianity.
The dragon episode is a later legend rather than a securely documented event from his life. Early versions of the story were associated with Cappadocia; the setting was later transferred to Libya in the 13th-century Golden Legend. In the tale, George rescues a princess and defeats a dragon threatening her community.
The image of the mounted warrior became especially influential after the Crusades. Saint George is normally shown on a white horse with a lance, while the red cross associated with him became a prominent emblem in England and other places. Saint Michael is also portrayed defeating evil, but he is an archangel, not the Roman soldier in this question.