It's often described as the temple of Diana it seems, but this is not attested and current thinking is it was dedicated to the Emperor Augustus, who was declared a god after his death in 14 CE.
The temple was knocked about by the Visigoths in the 5th century. In the Middle Ages it became part of the city's castle, and then in modern times it was gradually restored to what we can see today.
Évora is a very interesting name etymologically; ebora meant "(place) of trees" or perhaps "(place) of yew trees" in the language of the pre-Roman Celts and has survived with little change to the present day.
The same root is the origin in the city name of York, although it has been modified much more. You can read about its long winding journey on Wikipedia and elsewhere, but here's the story.
The Romans Latinised Ebor or Ebora to Eboracum, which the incoming Angle and/or Saxons thought was Eoforwīc, from Old English eofor = wild boar and wic = village (an element found at the end of dozens of modern English place names, typically as -wich).
But later Vikings established a colony there, and changed the name to Old Norse Jorvik, the first element of which is recognisably the same as – cognate with – eofor, followed by -vik, which meant something like "inlet". So by now we have got from Yew Grove to Wild Boar Cove. Eventually of course this was shortened to modern-day York, and there you have it.