According to Api Version Set - REST API (Azure API Management) | Microsoft Learn, you can view Version Sets and update the name and description to your choosing. If you're not seeing this experience after selecting the APIM version, let me know.
Another option is to use Api Version Set - REST API (Azure API Management) | Microsoft Learn instead. There are update method is the same as the create method, which accepts a body response like
{
"properties": {
"displayName": "api set 1",
"versioningScheme": "Segment",
"description": "Version configuration"
}
}
But it doesn't have a property for the version set name. I have to confirm, but for Q2, since the version set name is maintained by the service by using the display name and version scheme, it can't be customized. I agree with you on Q3, but I think you can use still use the update REST API to update the display name and/or versioning scheme which should reflect in the version set. I can pass this feedback along to the product team and see if and how it can be addressed.