His middle name is... wait for it...
Problems I'll state up front: not that obscure, projection?, and what astronaut? Otherwise, my better reasons, ignoring what I believe are ornamentations.
The name that you seek is both first and last.
It was once more popular in the past
Definitely used as both a first and last name.
Many who are famous have enjoyed the name
Here are a few.
But whoever possessed it never took the blame.
Lots of people didn't take blame. Ornamental. It could mean since their parents named them they didn't have a choice.
Whether painters, drivers, murderers, or geographers,
Doctors, lawyers, chemists, or hooks,
Politicians, sociologists, astronauts, or books,
All seemed normal, just like a cook.
Cook is the most important, but other occupations are covered; from the wiki link "This led to the word being given as a last name to people who worked in or near a garden. Later it came to be used as a first name."
Sooo... off to the store you must go
To find the clues that will lead to success
For projections are the key to solving this riddle
And it will be in a place that has a hearth and no bell.
Garth rhymes with hearth without a 'ding' G. But... I have to say... projection? Having difficulty with that. But hearth here could be another cook (e.g. garden?) reference.
You will laugh and cry as you search the anals
For the past holds the key and it ain't in Google.
So gird thy loins for task at hand
Cause it might even have something to do with a band.
Garth Brooks or Garth Hudson who was a member of The Band
I wish you luck as you embark on the quest
And I hope that you will finally be the best.
For it has been many years since task was last tried
But thankfully back then no one died.
Just a final comment, I think this history teacher (indicated at Reddit), probably took some liberties to make the rhyme and content interesting at the expense of perfect clues. Things like, hooks (which is probably just humorous), and drivers - neither of which would be verifiable for a name (or rather, significant, and also why it may just be that there isn't an astronaut either... maybe), and possibly the entire last verse.
But, they probably also didn't foresee a level of scrutiny seen here (they were just handing it out to a class for fun). Given that, I would expect that not all the clues fit, or fit perfectly. Hopefully, they will unveil their identity soon.