Hybrid parentage order influence on hybrid naming

[wogx]

Some time ago I've spotted a Rlc. "Terepaima" on a vendor's list. I always thought that a "Terepaima" is a Cattleya maxima × Rhyncholaelia digbyana cross. But it wasn't that case, it was a Rhyncholaelia digbyana x Cattleya maxima var. rubra. Was it correct, or someone wanted to increase their sales by using a well-known name? Should we differentiate an A x B cross from B x variety of A? Wouldn't it be ideal to track a cross deeper, using exact names of used cultivars (e.g. Cattleya rex 'Inti' x Cattleya maxima 'Chadwick's Dark')?