If it is your name then as far as the IRS is concerned, it is yours. The financial institution report to the IRS the SSN that is listed on the account.
Why is that not your father if it is his investment? Who receives the dividends?
If this is a joint account and you are on it simply for inheritance purposes and your father receives all the dividends then he should be listed first on the account so he (and his SSN) receives the dividends and 1099-DIV. If your father received the dividends then he must amend to report them even without the 1099-DIV.