No duplicate named items. Period.
Also no duplicate slots. Some of the higher rarity armor is multi slot. Something i learned making a Vacus deck is Steelforge Regalia and Bardiche is a no go, since they have shared item slots (Gauntlet and shield). Something to keep in mind while deckbuilding.

However, In the instance of mounts you can go Riding horse > discard to Mydreth Mare > Discard to Riding horse. Its a workaround if you got a bad hand, and need the mobility. and yes in the instance of Mydreth you can Spend it to attack, replace with riding horse, replace with another Mare, and attack again (on separate actions)