I lucked into two of Vera's outfits (I think because I wore one).
When I left I gave one to Cass, and the two of us look like top notch gangsters.
I have however finished Cass's quest line, and when I took her gear to fire her and hire V. I noticed I only had one suit on me...
If I fire Cass with the dress on her, and hire V. when I am done with V. and wish to rehire Cass will she have the dress, and other items still on her?
I seem to always pick one NPC, and stick with them, but this run I want to do them all however I plan on finishing with Cass, and would like her to look... stylish with me in New Vegas.

Sometimes, items in your inventory and inside containers will overlap and will not stack properly.
In other words, you might have 2 of the same item there but only one is showing, without the proper count indication on its side.
And yes, companions do retain items in their inventory when you dismiss them. You will be able to retrieve the items
at the time you ask them to join you again in your trips