Following up on farktronix's suggestion, we have been using Jira ticket numbers for similar in mercurial, and I'm planning to continue using them for git branches. But I think the ticket number itself is probably unique enough. While it might be helpful to have a descriptive word in the branch name as farktronix noted, if you are switching between branches often enough, you probably want less to type. Then if you need to know the branch name, look in Jira for the associated keywords in the ticket if you don't know it. In addition, you should include the ticket number in each comment.
If your branch represents a version, it appears that the common convention is to use x.x.x (example: "1.0.0") format for branch names and vx.x.x (example "v1.0.0") for tag names (to avoid conflict). See also: is-there-an-standard-naming-convention-for-git-tags