My grandfather was born in Ohio in 1909.
He was said to have changed his name at the age of 17 and left home.
I know he had siblings, but not the names of any of his family.
How would I find out his birth-name?
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At least 3 approaches are possible and should be used in conjunction.
Order your grandfather's SSN application (form SS-5). He was born more than 100 years ago, so his parents' names (assuming he included them) should not be redacted. Probably a more precise birth location would be recorded. If the application dates before he changed his name, the date that was official would be included. [See Ordering the SS-5, for good background information before going to the SSA website]
Follow your grandfather's records using his changed name backwards to find when he first started using that name. Verify the family story that it happened at age 17. Don't forget to include newspapers, as he may have remained in contact with someone from his family or hometown.
Using the exact birthdate you have, examine the Ohio birth record databases at ancestry, FamilySearch, etc. Using the full names, check the SSDI databases to rule out those that continued to use their birth name and those that don't match your grandfather's death date. Follow names through other early records to find if/when they disappeared. (Luckily you are dealing with a male; tracking females is complicated because of name changes following marriages).
A previous question, Finding orphaned grandfather's original surname? was similar but more generic.
You will stand the best chance if he only changed his surname, not his forename(s), and if you know the names of his immediate family (ie parents and siblings). That way you can find him by process of elimination - look in the census record for when he was a child for all instances of the parents' and siblings' first names all living together and with the right ages. If one of the forenames of parents or siblings is uncommon, it will make your task easier - look for that one first.