The ring can be swapped as many times as one desires but the spider will disappear or reappear when the ring is taken or inserted. Only then is the Dragonborn rewarded the Ring of Namira, which is required as payment to the new Namira's Altar to spawn this unique companion. Namiras Gift can only be spawned if the Dragonborn successfully completed the Skyrim quest The Taste of Death, and has chosen the path of a cannibal.
Once spawned, Namira's gift can be located at the base of the Altar of Namira inside the Daedric South Tower. Namira's Gift is a unique spider added by Castle Volkihar Redux. The spider is enhanced to be a far better combatant than its vanilla counterparts. It is solid velvet black in color with glowing green eyes.