question

If there is a customization exposed to do this I don't know what it is. But the headers are all available via the Response.Headers property in the controller. So all you really need to do is change the value at some point in the pipeline.

public IActionResult Index()
{
    Response.Headers["Server"] = "Mine";
    return View();
}

Of course you probably want to consider doing this in middleware or something instead of in every action.

@DeepakKumar-8706, Adding to cooldadtx on a similar lines -

On App Service when you perform any security testing, the result response is received from the frontends and never arrive to the actual worker (for example, invalid request).
Currently, if your requirement fits, you can App Gateway/WAF similar proxy in front and strip out the response header there. If it’s an enterprise app, it’s a good practice to have the WAF either way.

Please check this doc - Common scenarios for header rewrite

We have a UserVoice post on a similar request, ‘remove server header from the front end servers’ - you may wish to up-vote.

Also, up-vote ‘create custom error pages’ Uservoice post with a similar request.
Ref: similar discussion.

To benefit the community find the right answers, please do mark the post which was helpful by clicking on ‘Accept Answer’ & ‘Up-Vote’.