Guessing this is your ancestry tree here www.ancestry.co.uk/family-tree/person/tree/181785160/person/222361126189/facts
Have you considered the possibility that your grandfather may have been called after his reputed father?
From your tree and the image of his birth reg in 1909, he was called Andrew McMinigle Toehill.
McMinigle is not that common (even with variants). There is this entry for example in 1911:
Andrew MCMUNIGALL, aged 22
644/7 12/ 6
Possilpark, Lanark
Maybe this entry from 1901?
Hugh McMinigal 49 carter b. Paisley, Renfrewshire
Christina McMinigal 42 b. Glasgow
Nellie McMinigal 17 chemical worker b. Glasgow
Andrew McMinigal 13 b. Glasgow
Address: 506 Dobbie's Loan, Glasgow/Milton
Just thought to mention as a possibility 
Monica
Hi Monica!
Yes that's my tree. Andrew McMinigal is actually the adoptive parent of Andrew (McMinigal) Toehill along with his wife Catherine (Kate) McCleary.
I've definitely considered that Andrew or one of his brothers were the biological father because of the surname being on the birth record.
My DNA hasn't come back yet so can't see any matches but fingers crossed and will def update my findings!
Quoting myself here because I think I found out why my grandad was named after his adoptive father.
So, one of the first records, other than birth record, that I found for my grandad was his baptism record. The address was 25 Muse Lane. At the time I noticed there was another record on the same page as my grandad's also with the address 25 Muse Lane but just kind of shrugged it off.
A few months ago, I went poking around the birth and death records of my grandad's biological cousin. The only reason I did this was because she was born and died in the same year as my grandad. Anyways, this cousin was the daughter of my grandad's biological uncle (birth mum's brother) and the address on her birth record was 25 Muse Lane, same as the address on my grandad's baptism record.
So as I was trying to connect the dots, I went back to that baptism record, looked at the other record with the address 25 Muse Lane and saw the mother's maiden name as "McMinigle" - basically this record was my grandad's adoptive father's niece. No idea how I didn't notice this before.
My grandad's biological uncle and the sister of his adoptive dad both lived at 25 Muse Lane at the same time. And I guess that's where his adoptive parents also lived. His adoptive parents were neighbours with his birth mum's brother. Filling in the blanks, I guess there was an agreement before the birth that they would take him which is why he was named after his adoptive father.
The answer was literally staring me in the face.
