Not possible from the core's UI. The tag is basically just a word that is referenced by the post. The best approach to follow would be to remove it and add a new tag.
If you know SQL and understand how the tables are linked you would be able to do so. However, any other post referencing that tag will change too. In fact, due to denormalization, you won't see it if you just change the word in the words table because they are duplicated in the posts table but you'd see it if the question receives an update as the tags are usually recalculated (or I think if you reindex the content too).