I feel like especially together they would've been too conspicuous to go unnoticed for the ride to Minas Tirith. He's short, and she'd be noticed as shifty and wanting to go oddly far away to take a leak. They probably had to make sure they were around different people each night so as to not build on suspicion
shareThis is covered a bit in the book. There's a sort of "understanding" between Eowyn and the captain that they kind of just ignore each other. Nobody talks to her or Merry and they do the same.
In the film, they don't cover it (can't blame them - these things are packed to the gills and still run 3-4 hours each), but I can pretend it's happening off-camera.
If you want an explanation that isn't reliant on the book, I'd assume that Eowyn shifts around, both on the ride and in the camp, so everybody kinda thinks, "Hey, I don't recognize that guy...must be with that other unit over there..." and then forgets about "him" after "he" rides out of sight. Merry probably just keeps *super* low in the saddle, Elven cloak of Lorien on, and winds up looking an awful lot like a saddlebag.