Different mints can cross-pollinate one another, but you can prevent it from happening by snipping off flowerheads before they bloom. It would only be an issue if you saved seed and planted it, or if you let the plants go to seed and self-sow. So, if you planted a chocolate mint next to an apple mint, would you get a chocolate-apple mint from cross-pollinated seed? Maybe, but maybe not. Probably some seedlings would be crosses, but only a percentage. This tendency to cross easily explains why most mints are grown from cuttings instead of seeds. Each plant will retain their own flavor and characteristics in the current year, though, no matter what you do.

The bigger issue is that whichever mint is the most vigorous would undoubtedly crowd out any mint that is less vigorous. That is likely to happen with mints grown closely together.

You can put the mints in individual pots. Even better, put each mint in a pot and then sink that pot into the ground, leaving about an inch or two of the pot above the soil surface. (Mulch can hide the part of the pots that is above ground.) Sinking the pots into the ground keeps the mints neatly contained but also keeps the roots cooler and thus they'll need watering less often. You will have to keep an eye on the mints because they will try to root into the mulch and grow there once they reach a decent size. (If you let them root just a little, you can break off the rooted portion and you'll have a new plant to put elsewhere or to give to a friend.)

Dawn