Back in the day, I was huge into Jane Austen and Georgette Heyer, and lots of their modern-day sisters. Which meant learning about nobility, because 95% of modern Regency romances involve titles for one or both of our protagonists. Is it correct to call our hero Lord Hadrian when he's only a Baron? (No, he'd be Lord Potter.*) Once Ginevra marries the Duke of Thingy, is she Lady Ginevra? (No again - she's Lady Thingy, "Your Grace" for formal.*)
...so basically, dear people who are writing Harry Potter wish fulfillment fic wherein he inherits All The Titles? Harry will
not, in fact, wind up as Harry Potter Black Peverell Slytherin Gryffindor Extra, and no self-respecting goblin would call him that, even to wind him up. (Well, maybe
just to wind him up.) He would be Harry Potter, Duke of Peverell, Marquess of Gryffindor, Count of Slytherin, Viscount of Black (to arbitrarily designate actual titles), and he'd be called Lord Peverell, with all the rest just sort of...elided underneath, no matter how rich and important they are.
(I enjoy a good wish fulfillment fic as much as the next person! But after the third or fourth or twentieth fic that thinks inheriting titles means piling on the last names, I just...yeah.)
*
On the off chance that any of y'all are curious, I checked my memory here.