We don't know of anyone who chose to go into Hufflepuff.
To answer the main question first: no, I'm not aware of any Hufflepuff who specifically told the Sorting Hat to sort them into Hufflepuff. Indeed, we don't hear any information in canon about why the characters in Hufflepuff were sorted into the house they ended up in.
It's conceivable that this may change if we hear more about Newt Scamander's sorting in future Fantastic Beasts films.
I don't think that it's at all unlikely that kids did decide to go into Hufflepuff, though. The idea that Hufflepuff is the 'leftovers house' is probably based on the following quote from the Sorting Hat.
For each of the four founders had
A house in which they might
Take only those they wanted, so,
For instance, Slytherin
Took only pure-blood wizards
Of great cunning, just like him,
And only those of sharpest mind
Were taught by Ravenclaw
While the bravest and the boldest
Went to daring Gryffindor.
Good Hufflepuff, she took the rest,
And taught them all she knew,
(Order of the Phoenix, Chapter 11, The Sorting Hat's New Song).
I think it's fair to say that this means that Hufflepuff is less demanding in who it lets into its house. It's less elitist and more willing to give those students who aren't in to showboating a home. That isn't to say that it's a scrapheap which no student would ever wish to be associated with.
Of course, there are some - like Malfoy - who wouldn't consider it.
"Well, no one really knows until they get there, do they, but I know I'll be in Slytherin, all our family have been - imagine being in Hufflepuff, I think I'd leave, wouldn't you?"
(Philosopher's Stone, Chapter 5, Diagon Alley).
Malfoy, however, is hardly a neutral on this subject. As he says himself, he clearly knows what house he'll be sorted in and indeed he was sorted into Slytherin the moment the hat touched his head. Some students may have avoided Hufflepuff but others may well have aspired to it. Just look how its qualities are described by the Sorting Hat.
You might belong in Hufflepuff,
Where they are just and loyal,
Those patient Hufflepuffs are true
And unafraid of toil,
(Philosopher's Stone, Chapter 7, The Sorting Hat).
Could you honestly say that you wouldn't want to be described as fair, loyal, patient, trustworthy and hard-working by your friends and family? Would you prefer to be seen as a foolhardy (Gryffindor), scheming (Slytherin) smartarse (Ravenclaw)?
Hufflepuff may be the wimp house to some. But many others could conceivably have seen it as the best option and the house with which they were most keen to be associated. Cedric Diggory, for instance, placed great value and honour on the principles of fairness and good sportsmanship. It's entirely believable that he would ask to be put in Hufflepuff.
Anyway, it's a matter of fact that Hufflepuff isn't literally a leftovers house - a place to put miscellaneous students when the other houses are full. Hufflepuff was the house picked by the Sorting Hat for the first two students on its list, not the house chosen at the end in order to make up the numbers.
"When I call your name, you will put on the hat and sit on the stool to be sorted," she said. "Abbott, Hannah!"
A pink-faced girl with blonde pigtails stumbled out of line, put on the hat, which fell right down over her eyes, and sat down. A moment's pause -
"HUFFLEPUFF!" shouted the hat.
The table on the right cheered and clapped as Hannah went to sit down at the Hufflepuff table. Harry saw the ghost of the Fat Friar waving merrily at her.
"HUFFLEPUFF!" shouted the hat again, and Susan scuttled off to sit next to Hannah.
(Philosopher's Stone, Chapter 7, The Sorting Hat)*.
It's likely that at least some of the students of Hogwarts wanted to be in Hufflepuff enough to ask the Sorting Hat to sort them there. We just don't have a clear-cut example to prove it.