I recently changed the company, what should I do with my Atlassian account?
It's an unmanaged account. Should I change the email address, ... or should I delete the account and create a new one?
For an unmanaged one, yes, just change the email address - that way you get to keep everything you had associated with the account (even though your company are probably going to remove you from their systems). Stuff like your kudos and badges here belong to your Atlassian account.
It's also a lot easier than delete and create new.