is it possible to change lightsail static-ip's resource name?

Probably cannot be changed.
The IP address will change, but if you want to change the name, you will need to re-create it.

I checked the Lightsail API documentation below and there is no API to edit the IP address, so I don't think it can be changed.
https://docs.aws.amazon.com/ja_jp/lightsail/2016-11-28/api-reference/API_Operations.html