For all resources, you can change the Pulumi name without effect, so long as you also add an alias opt back to the original name. However, this has no effect on the provisioned resource, only on the Pulumi state.

For all provisioned resources, the answer depends on the type of resource.

For example, you cannot rename an S3 bucket. AWS does not support that at all. Impossible.

You can easily rename an EC2 instance though, because it's just a tag with key "Name".