The patient who entered a Shreveport, La., hospital for surgery earlier this month was registered as ''Thomas Brady'' and his medical condition was likened to ''tennis elbow.'' But the name was an alias, his doctor revealed yesterday, and the ailment was an analogy.

It could more appropriately have been described as ''football elbow.'' For the man Dr. Bill Bundrick really operated on, he said, was Terry Bradshaw, the Pittsburgh Steeler quarterback. ''He's doing well,'' Dr. Bundrick said, noting that Bradshaw had been released from the hospital a few days after surgery to repair tears in the muscle near his right elbow. ''It's the same thing as tennis elbow,'' said Dr. Bundrick, who disclosed that Bradshaw had suffered from the condition for about a year. Dr. Bundrick said Bradshaw would be able to start throwing a football in June and should have no further problems with the elbow.