Users frequently have custom domain for their blogs in Tumblr. If you need to know the [Tumblr] username from the custom domain, just need to grab the value from the header field
$ curl -Is blog.foursquare.com | grep -i x-tumblr-user X-Tumblr-User: foursquare
$ curl -Is blog.birchbox.com | grep -i x-tumblr-user X-Tumblr-User: birchbox
Now you can use the username to make some API calls to Tumblr.