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I always learned Gagarin was first into space first. Likewise, I learned Shepard was the first American and Glenn was the first American to orbit the Earth. (I always have to stop and think about Grissom, since the fire of Apollo 1 is the always first thing that comes to mind.)

Saying that someone has to orbit the Earth or do something while in space in order to be an astronaut seems like changing the definition. That would mean Shepard wouldn't become an astronaut for another 10 years. (Of course, then he would be in a very select group of astronauts, because he had walked on the moon.)