I would think that money paid to a child over 18 is that child’s. Probably different if the recipient is under 18, then it would bw held by the parent in a fiduciary capacity, and have to be spent for the child. But if it is the child’s own money, there are no restrictions on what s/he can spend it on or do with it.
If that is correct, then these benefits would be income to the child. On the other hand, if the checks were made out to the parent, NOT “for the benefit of” the child (or other similar language indicating a trust or fiduciary capacity), then it would be income to the parent. You will know for sure when you see the SSN on the 1099. Either way, it should be reported as income of one or the other on FA forms. Can’t get around that. It is income to someone, and the tax rules will dictate who reports it on their tax return.
Now if it was income of dad, and dad gave it to OP, then as a gift it would be reportable as untaxed income of the OP. However, if OP never spent any of it, s/he could possibly return it to dad and say that the transfer was a mistake, or that s/he never “accepted” the gift. Can’t do that if OP spent any of the money, though. Of course then it’s dad’s money, no strings attached.
If it was income to OP originally, there is nothing stopping OP from GIVING it to dad. OP would report it as income, but not as an asset, if it is given away before FAFSA is filed. There is no penalty for giving away assets prior to filing FAFSA, like there is when planning for Medicaid to pay for nursing home care. There can’t be any plan to give back, of course, or it is not a real gift, but I thought the OP was asking about a true gift to dad.