An unacknowledged partial title drop for that movie is that "Lord of the Ring" (with no s at the end) is uttered.
In chapter one, Many Meetings, Gandalf tells Frodo:
> Yes, I knew of them. Indeed I spoke of them once to you; for the Black Riders are the Ringwraiths, the Nine Servants of the Lord of the Rings.
And in chapter two, The Council of Elrond, Glorfindel says:
> And even if we could, soon or late the Lord of the Rings would learn of its hiding place and would bend all his power towards it.
In the final chapter (The Grey Havens) of book six, the Red Book is also titled by Frodo “THE DOWNFALL OF THE LORD OF THE RINGS AND THE RETURN OF THE KING”. Now there’s a title drop.
(Just in case it’s not obvious: I’m talking about the books here, not the movies. Never seen ’em.)
Found the quote by googling, he was scolding Pippin, not Frodo, and it was "Ring" singular after all:
> "Hurray!" cried Pippin, springing up. "Here is our noble cousin! Make way for Frodo, Lord of the Ring!"
> "Hush!" said Gandalf from the shadows at the back of the porch. "Evil things do not come into this valley; but all the same we should not name them. The Lord of the Ring is not Frodo, but the master of the Dark Tower of Mordor, whose power is again stretching out over the world!"
(Book II, Chapter I)