How is puppy play humiliating for a sub?

So I've been living with my partner and he is something of a switch he's my slave but he dominates professionally and he has three "dogs" that's what he calls them usually what happens is that I end up taking the dogs for walks while he works on something else and I don't really know their names I call them Spot, Rover, and Fido. Fido's my favorite but I don't tell him.

Anyway I'm just curious how is it humiliating for them because whenever I'm taking them out for "walks" I feel embarrassed and humiliated because I don't even like this kind of thing (I do it because well I'm pregnant and unemployed and I can't find a job and I hate feeling useless) and because they are in suits and masks it's like at least nobody knows who they are where as with me it's like anybody could see me and know who I am. I just really don't get it I feel like I'm the one who should feel embarrassed.