My father died when I was 2 months old I'm 25 and have been trying to find out since I was 13 . I got his death benefits growing up.. My father deserves to be on it I am his only child he died when he was 20 . Please someone help because oregon's help system sucks..

Why do you think it matters? Even if you could do it, it makes absolutely no legal difference.

... My father deserves to be on it I am his only child...

Get him a nice tombstone. A birth certificate is not a monument.

Your birth certificate is for you and your parent(s) only. Write his name on your copy. You can't change it in the records.
Find out all you can about him, and write it down for posterity, with pictures if you can find any, for your children and grandchildren someday. Put it on your Facebook or make one for him, or include it with your mother's.