How do you rename the machine name of a content type?
I disagree with most of the comments above simply stating: don't change the bundle machine name. These don't answer the poster's question.
This was a simple task in Drupal 7; but due to the added complexities in Drupal 8 it was decided to attempt to remove this ability. See this issue for history:
#2172843 Remove ability to update entity bundle machine names.
That being said, if you do a database search/replace on the machine name this should do what you are looking for - BUT beware, some of those machine names are embedded in serialized data (e.g. key_value table) and you will need to modify the json string size if the machine name you are replacing is a different length than the new name.