Changing the integration name will most likely cause your scopes to stop matching (because the integration name is part of the target path used in the Target rule of scope rulesets).
If you must change the integration name, look for all scopes that have rulesets that includes this integration name in the Target field, and change the Target selector in all such rulesets.
You may want to follow this flow:
1/ Clone existing scope
2/ Modify to use the new name you want to use
3/ Update integration name
4/ Disable old scopes
5/ Test and ensure scope matching still happens as expected