A name's token ID changes in exactly three cases: a role on the name is granted or taken away, the name expires and is registered again, or the name is unregistered. A role is a permission that lets a wallet act on the name. When a role changes, you still own the name.
What a token ID is
Every ENSv2 name is an NFT (a token you hold in a wallet). The token ID is that NFT's number. To see it, open the name in ENS Explorer. Then choose Token info in the sidebar.
When the token ID changes
When a role changes, the old token is swapped for another with a different number.
Other actions do not change the token ID. These include setting records, renewing, changing the resolver and sending the name to another wallet. Changing roles on the resolver does not change it either.
What stops working after a token ID change
A marketplace listing made for the old token ID ends. To keep the name for sale, list it again after the role change.
This is on purpose. It stops a name being sold under an old listing after its roles change.
Common questions
Did I lose my name when a role changed?
No, a role change does not lose your name. You still own it.
Can I stop the token ID changing?
No, you cannot stop the token ID changing when a role on the name changes. If you plan to list the name, finish any role changes first.
Does sending my name to another wallet change the token ID?
No, sending your name to another wallet keeps the same token ID.
What should I use to keep track of my name?
Use the name itself, such as yourname.eth, not the token ID. The name stays the same, but the token ID can change.