You get the carrier name and tracking number from your third-party, usually. If you mean, you want to query an existing fulfillment and get the carrier name and tracking number assigned to it, then that is not a mutation, but instead, you get the value by providing the ID of the fulfillment you are interested in. A quick scan shows fulfillmenttrackinginfo when you get a fulfillment.
So if all you have is a tracking number, you're out of luck. You need the order, to get the fulfillments, and then match your tracking number to one of those results.