I think at least from a music theory standpoint the sharps and flats IN a key signature ARE the key signature and are referred to as such. For example, there is no key signature with just a C#. There is, however a key signature with an F# and a C# and it is know as the key of D major/B minor. There is no other key signature with two different sharps. For that reason I think the two sharps themselves become a symbol for the key of D major/ B minor and are not just viewed as an F# and C# (though they are in the key signature itself).
So individually I don't think they have a name, but together make up the name of a key signature.
Kind of like an 'F' itself is on long vertical line and two short horizontal lines in a certain pattern. We don't really see the lines, just the F itself even though it is made up of all those lines.