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.

There is a way** to add the 1099-div and show the income is not yours.  But you can only do that if you know the other person has reported the 1099-Div on his return.

Since your father has not reported it, then you must report it on your return.  Furthermore, the situation you describe means you did actually receive the money (it was reinvested in your account).

**After entering the 1099-DIV, in TurboTax (TT), you will reach a screen "Tell us if any of these uncommon situations apply to you".  Check "I need to adjust these dividends", then continue.  At the screen "Tell us about your dividend adjustments", enter the amount and check "I received all or part of these dividends for someone else (I was a nominee)".  TT will show the adjustment on Schedule B