Is CR a must to update stake holder register if identified in later stage?

Is CR a must to update stake holder register if identified in later stage?

Stakeholder register is an internal document in the project management plan'
Unrelated to the scope , time ,...etc
If you discover a new stakeholder it would be awkward to initiate a CR to add him in the register.
You may include it in the issue log though

is that not a repsonsibilty and a procedure a PM shud follow to update stk register?