"The Roman Army" is a name given by English-speakers to the soldiers and other military forces who served the Roman Kingdom, the Roman Republic and later the Roman Empire. The military forces in general were the militia, and a commander of military operations, magister militiae. In the republic, a general might be called imperator, "commander" (as in Caesar imperator), but under the empire, that term became reserved for the highest office.
The Romans only called themselves "Roman" in very formal circumstances, such as senatus populusque Romanus (SPQR), "the senate and people of Rome" or when they needed to distinguish themselves from others, as in civis Romanus, "Roman citizen." Otherwise, they used less formal and ethnocentric terms, such as nostri viri, "our men", also in mare nostrum, "our sea", for the Mediterranean. The state was res publica, "the public thing", and parallel to it was res militaris, "the military thing", which could have a number of connotations.