Well, first of all they would not have called themselves Vikings. In Norse as well as old English, Viking means Raider or Pirate. It was a description of their actions, not a description of their origins. Although the word Viking existed in Old English (as well as Old Norse) it had died out by Middle English. It was re-introduced to the English language in the 1800's during the viking revival. There are several contemporaneous gravestones in Sweden that have the epithet Viking added to their name, for example Tóki Víking (aka "Tóki the viking").

Another common name for them "Norse" or "Norsemen" means simply "Men from the North". Once again this was a term applied to them largely by their victims. Interestingly, when latinized Norseman (or Northman) becomes Normannus, which will eventually lend its name to Normandy. It also becomes Norway. This term was a common description in Latin texts, especially by the Frankish priests in what would later be France.

In Ireland they were called Ostman, or Eastman (men from the East). The Icelandic Sagas sometimes use this term for men from Norway.

The Anglo-Saxon Chronicles, which are contemporaneous with the viking invasion on England (written from the late 800's to 1154), generally refers to the invaders as Danes. The area that the vikings occupied was said to be under "Danelaw". They do make several exceptions, for instance saying that a Dane army "were joined by men of Frisia".

The Norse also traveled up the Volga river and called themselves Rus. It is from there that we get the term Russia.

The Norse were made up of men from several different kingdoms. They were made up of Frisians, Geats, Danes, Gutes, Swedes, etc, and probably would have referred to themselves as such. At times they would be unified into one or more kingdoms, for instance Cnut the Great unified England, Denmark, and Norway. At other times these kingdoms fell apart and people went back to being Geats and Danes, etc.

So the term Viking (Norse vikingar, old English wicing) was a job description. They probably thought of themselves as Viking Danes (or Viking Rus, etc). Their victims called them by a great many names, among them Norsemen, Ostman, Danes, Vikings, etc.