versor
Noun
Meaning
The turning factor of a quaternion.
Source: Webster's dictionaryExamples
Either may be used to build general versor operations, but the former has the advantage that it extends to the algebra in a simpler and algebraically more regular fashion.
Perwass also claims here that David Hestenes coined the term "versor", where he is presumably is referring to the GA context (the term versor appears to have been used by Hamilton to refer to an equivalent object of the quaternion algebra).