This system is not fully implemented in the PTR 5.2, but build 16486 added cosmetic changes that suggest players who queue to Random Dungeon LFG can choose which reputation faction they wish to gain reputation points with.

In the Random Dungeon LFG window and Scenario window, there is a red button which says: “Choose Reputation”. Clicking that button opens up your character window’s reputation tab.

At this point, PTR players can’t yet choose a reputation. Work in Progress.

patch-5-2-random-dungeon-reputation-changes

Eldorian linked me to a blue post concerning this new feature:

As the PTR Patch Notes read currently, it’s the first dungeon and first scenario. Of course, things might change, but that’s the plan right now.

The answer was/is so blooming obvious, you never had to re-invent the wheel, just put the old one back on – simply having both at release (instead of removing tabards) – Blizz could of scored a blinder by satisfying everyone – missed opportunity by not keeping tabards with the current daily system on release, missed it again in 5.1 and instead opt for a watered down fix in 5.2.
If one of them is the obvious path to get it done faster, the developers have seen over the years that the players will take that path, even if it’s something they just don’t like doing (which is probably why some people feel dailies are mandatory, because they’d like to spend their valor points on that gear rather than using the item upgrade system, perhaps because the’ll spend them better there).

Also, keep in mind that in 5.2, valor gear will have a reputation requirement, but this reputation won’t be earned from daily quests (which will also be available and it’s a different faction).