The name '

Geometric algebra' is preferred when the

geometric
properties of the system are emphasized. This is usually desired in

physics,

engineering and other

applications, because this algebra helps people

visualize the problem and understand it in a more

tangible way.

On the other hand, an algebra as such is completely abstract. All possible calculations of Clifford algebra can be done on an abstract level, for example in a matrix representation. If this is sufficient, it is quite pointless to use geometric algebra in the first place.