If you want the bucket to have the same name, then you are going to have to do exactly that, since bucket names have to be unique and AWS creates all sorts of bindings when a new bucket is created and it takes awhile to de-provision them.
Here’s the docs on how Cloudfront handles regional Edge caching ( see “How CloudFront works with regional edge caches” )
https://docs.aws.amazon.com/AmazonCloudFront/latest/DeveloperGuide/HowCloudFrontWorks.html
Unless you absolutely need that bucket to reside in the new region, I highly recommend the CloudFront distribution. They also work seamlessly with AWS certificate manager so you can create custom CDN domains.