Bombur, Gentle Dreamer

Storied isn't a triggered ability and doesn't use the stack. Players can respond to a spell that will give you your third legendary, Saga, and/or artifact permanent, but they can't respond to you getting an enduring story once you control that third permanent.

If you control three legendary, Saga, and/or artifact permanents but don't control a permanent with storied, you don't get an enduring story. For example, if you controlled three artifacts, lost control of two, then cast Thorin Oakenshield, you won't have an enduring story.

A single permanent can only count once toward the three legendary, Saga, and/or artifact permanents needed to get an enduring story, even if it has more than one of those qualities. If you control one permanent that is a legendary artifact and a second permanent that is a Saga, you will only have two of the three permanents required to get an enduring story.