Please help me figure this out because I've been searching for it for months and still no clue !

I believe it was because the father had walked out or divorced their mom by the time Michael was born. Besides it turns out later Lincoln was not Christina Scofield's son.

It's correct, it was because Aldo walked away from them. Michael was born September 8, 1978. His father abandoned the family before Michael was born and so he chose to take his mother's maiden name. Lincoln was born 6 years before so he still kept the Burrows name.

link was adopted after his parents were killed micheal,s dad took him in