Naming primaries is generally no different from naming any other hybrid (read this: http://www.firstrays.com/hybridregistration.htm
The only exception is if one has determined that the hybrid is a natural
one - that is, it occurred without man's intervention in an area wheere two species' ranges overlap. In that case, the hybrid typically has an "X" in front of it - Phalaenopsis xNatural.
I don't know the number that have been registered, but if there are 50 species, the maximum number of species x species primary hybrids would be 1224 (the first can be crossed with 49 others to give 49, the second can be crossed with 48 others, giving a total of 97, etc. - A x B is the sames as B x A for registration purposes).
A cross made using ANY hybrid is no longer considered "primary", but becomes "complex", although that term is usually used in the traditional sense when the hybrid has a lot of family tree under it. For your example, one often hears that the second generation hybrid is a "crossing of two primaries".