Tagging functional group
In the study of amino acids (and peptides, proteins etc), it IS standard practice to label the alpha carbon as such. More carbons leading into the R-group may also be labeled with Greek letters, but this is not as necessary as having a label for the stereogenic center, the alpha carbon. Personally, I've found Greek letters helpful in remembering the structures of the different amino acids, for example I always think of Lysine as "the one with the epsilon-amino side chain". Note that in chemistry in general, whose nomenclature follows IUPAC guidelines, it is NOT "standard" to use Greek lettering, however it is still generally recognized. The practice is probably most prominent in the study of fatty acids (another biochemistry subfield), which results in such Greek -rich categorizations as "omega-3 unsaturated fats".