If you don’t care about role_key value…

…it’s very easy to achieve that with wp-cli:

1. duplicate the existing role – $ wp role create new_role 'New Role' --clone=old_role
2. then delete the old one – $ wp role delete old_role
3. and last reassociate the user(s).

Otherwise…

…you can edit the serialized entry in the db. Wordpress stores the serialized array of roles in wp_options table. So:

1. Fetch the serialized array:
   SELECT option_value as serialized_string FROM wp_options WHERE option_name = 'wp_user_roles';
2. Unserialize the string – php: $rolesArray = unserialize($serialized_string)
3. Change the role name – php: $rolesArray['role_key']['name'] = "New name"
4. Serialize back the array – php: echo serialize($rolesArray)
5. Replace the db option_value content with output from the previous point

Actually, there are many ways to achieve that:

With pure php and mysql you can edit the serialized entry in the db. Indeed, Wordpress stores the serialized array of roles in wp_options table. 

So:

1. Fetch the serialized array:
   SELECT option_value as serialized_string FROM wp_options WHERE option_name = 'wp_user_roles';
2. Unserialize the string – php: $rolesArray = unserialize($serialized_string)
3. Change the role name – php: $rolesArray['role_key']['name'] = "New name"
4. Serialize back the array – php: echo serialize($rolesArray)
5. Replace the db option_value content with output from the previous point

If you feel confident with Wordpress, you can even use the embedded Wordpress REPL in wp-cli to fetch the stored value with get_option('wp_user_roles') and then use update_option to update it.

And (always) remember to backup the db before options manipulation ;)

Otherwise, if you don’t care about role_key value…

…it’s very easy to achieve that with wp-cli:

1. duplicate the existing role – $ wp role create new_role 'New Role' --clone=old_role
2. delete the old one – $ wp role delete old_role
3. then associate new_role to the user(s).
4. eventually repeat step 1 and 2 until old_role = new_role