How to determine client name inside handler middleware instantiated via HttpClientFactory

[sandersaares]

For purposes of logging/metrics, I want my HTTP message handler middleware to know which HttpClient registration it is being called from. For example:

services.AddHttpClient("foo", client =>
{
    client.DefaultRequestHeaders.Add("x", "y");

}).UseRequestLoggingMiddleware();

Where UseRequestLoggingMiddleware() adds some custom middleware I use. In this middleware I want to write log entries that reference the string "foo" provided when the HttpClient was registered.

However, I am unable to find any way to lookup the HttpClient name "foo" when in the middleware. How can I accomplish this?