Bisulfate vs Hydrogen sulfate
Nope, no rule, and again there is no difference, like your question about the names for iron oxidation states.  The "bi" form is the older form, and the "hydrogen" form is now preferred, again because it more explicitly describes the form of the compound.

EDIT: Some additional detail was requested.  When I say "preferred", I mean the name sanctioned by the IUPAC (International Union of Pure &amp; Applied Chemistry), also known as the systematic name, so called because the rules to form the name are "systematic"; i.e. consistent and clear. Older names are called common names, which were in used before the IUPAC.  So "bisulfate" is a common anion name, while "hydrogen sulfate" is systematic.