I started a Hardcore Solo character (both options on the left enabled when you create your character) and when ingame I then activated the Ardent Gladiator pet that you get to follow you around and when I died I deleted my character and then jumped into a new Hardcore Solo character and the pet is still there but its not showing in the “Cosmetics”-menu so I am now able to have two of them out at the same time.
Both characters with the same name if that matters any.