You're safe. Changing the name of a role has no effect on most of Jira. Workflows, permissions, report configs, security, notifications and so-on are all configured by using the role's unique ID from the database, which doesn't change. The name of a role is just an attribute of the role, it's for humans to have something readable to work with, not an identifier.
But, yes, of course your renaming will appear throughout Jira - roles are global objects, so changing their name will affect everywhere they're displayed.
The exception is where you've used it in a saved search (a filter). I doubt you'll find you've got any filters that refer to roles, but if you do, they might break (I'm really not sure that they will - I've never seen a filter that refers to a role, so I've never tested this).