Even for married joint owners, when the money does belong equally to both, the interest is only reported to the first listed SSN. Bank is required to report to the first named account holder so that’s what it does.
As far as the bank is concerned, joint owners are joint owners. Any owner can wipe out the account for the purposes the account was set up for or for other reasons. That goes for the creditors of the account owners too, who can attach the account for judgments, taxes, child support, etc. One owner can argue “Oh, but that’s not my money, it’s Granny’s” but usually the creditor doesn’t care and the bank can’t stop it (there are some exceptions for SS checks and other ‘protected’ funds, but as you can imagine it is difficult to separate these funds once they are co-mingled). If the OP wrote a check to pay her debts, not just Granny’s, the bank is not going to stop the check from clearing because it isn’t for the Granny’s benefit. The bank is not policing accounts.
The presumption for any asset is that it belongs to person it is titled to. The car titled to the parent belongs to the parent, not the child who drives it, pays for the gas, maybe even bought the car. The beach house belongs equally to the 6 siblings, even though only 4 of them use it and pay the maintenance on it because that’s the agreement they made. Title is going to overrule agreements.
FAFSA and CSS forms don’t ask for just assets that you feel you own, they ask for assets. No need for judgment on whether the asset is ‘really’ yours. 529 plans for other children have to be reported even though that money is not really the parents’ asset, will not be used for this student, deposits were made by third parties specifically for the younger child. Rules say report it, it’s an asset within the parent’s control. There is a way to avoid this, and it’s by putting the account into the name/control of someone else, like a grandparent. Financial gymnastics? Yes, but required to avoid reporting it.
The original question was would the OP be required to report assets held in her name. Yes, IMO, she must report all accounts in her name.