How was the Roman Empire officially referred to by contemporaries throughout the 1st to 6th centuries AD?

Question

I understand that the notion of state in the specified period was different from the modern one and maybe was gradually changing over time. However, I still believe that contemporary sources occasionally had some need to refer to the political organization nowadays called "the Roman Empire."

I presume that the Early Roman Empire (principate of 1st-3rd centuries AD) stubbornly continued referring to itself as the Republic of the Roman Senate and of Roman people, the idea that I assume, often was meant behind the abbreviation of S(enatus)P(opulus)Q(ve)R(omanus).

If so, was it the only way to refer to the state? Did it change with the transition to a seemingly more authoritarian political regime in Late Antiquity (from Diocletian onwards)? Did the spread of Christianity and increasing acceptance of it by the ruling elite influence the way contemporary sources mentioned the state?

Answer 1

Tacitus Agricola 29-32 on Calgacus's speech to his army of Britions/Caladonians where Calgacus referred to the (Roman) empire. "Robbers of the world, having by their universal plunder exhausted the land, they rifle the deep. If the enemy be rich, they are rapacious; if he be poor, they lust for dominion; neither the east nor the west has been able to satisfy them. Alone among men they covet with equal eagerness poverty and riches. To robbery, slaughter, plunder, they give the lying name of empire; they make a solitude and call it peace (ubi solitudinem faciunt, pacem appellant).

Also

Rome was used to refer to the roman state, not just the city. Coins were stamped with Roma.

Also these terms came into us after the first republic was established and SPQR appeared on documents.