The recommended name should be qualified in each instance by adding the name of the natural substance, e.g. maltodextrin phosphorylase, starch phosphorylase, glycogen phosphorylase.

Phosphorylases are important allosteric enzymes in carbohydrate metabolism. They catalyze the formation of glucose 1-phosphate from polyglucose such as glycogen, starch or maltodextrin. Enzymes from different sources differ in their regulatory mechanisms and their natural substrates. However, all known phosphorylases share catalytic and structural properties. They are pyridoxal-phosphate dependent enzymes; the pyridoxal-P group is attached to a lysine residue around which the sequence is highly conserved and can be used as a signature pattern to detect this class of enzymes.
Reference

Glycogen phosphorylase:

1,5-Gluconolactone is a very powerful reversible inhibitor of glycogen phosphorylase. Transition state analogue.

Phosphorylase a and b are an active form (GPa) and inactive form (GPb). From GPb to GPa is activated by AMP and IMP. Ser14 is phosphorylated by cAMP-activated protein kinase. Pyridoxal phosphate bound to Lys680 makes no mechnistic role, but a strucutral role. AMP and IMP are activator. Glucose-6-phosphate is allosteric inhibitor.

Domain 1: the regulatory domain (1-148). Organized about a mostly parallel, nine stranded, beta-sheet core. Two subdomains. Interface subdomain (1-315). Glycogen-binding domain (316-484).

Domain 2: contains a classical nucleotide-binding fold which is flanked by teo layers of helices. Catalytic site is located between domains 1 and 2.