What do you call this?

[ladymuck]

It depends. Usually the ordering comes from which was the male genetic donor and which was the female

So male dog, female fox could be a dox whereas male fox, female dog could be a fog. This is how it's done for the liger (male lion, female tiger) and tigon (male tiger, female lion).

Or you go by the ratio of the genomes in its DNA from each species.