Immediately after merging.
Branches are cheap in Git, and if you're keeping them around, you could be stuck in the SVN/CVS era. If you made a merge commit, it often contains the branch name. Even with fast-forward merges, branches shouldn't really be used to track historical data. That's what commit messages are for.
We often add the bug tracker ticket number to the commit message so that it can be referenced in the future. The branch pointer and its name are redundant in this case.
In fact, you can check out the repository with no other branch except the main one, and it would still contain all commit messages. That is the historical data. You can easily create any branch again at any commit you like, and you can change any branch information any time. But you mostly cannot alter the commit history without serious consequences.