Today I watched The Deathly Hallows and now I'm wondering about the tale of The Deathly Hallows.

Are the names of the three brothers known? If yes, who were they?

They’re Antioch, Cadmus, and Ignotus.

Xenophilius Lovegood tells Harry, Ron, and Hermione that the three brothers in Beedle’s “The Tale of the Three Brothers” were Antioch, Cadmus, and Ignotus Peverell.

“The sign of the Deathly Hallows on Ignotus’s grave is conclusive proof!’

‘Of what?’ asked Ron.

‘Why, that the three brothers in the story were actually the three Peverell brothers, Antioch, Cadmus and Ignotus! That they were the original owners of the Hallows!”
_{^{- Harry Potter and the Deathly Hallows, Chapter 21 (The Tale of the Three Brothers)}}

Though Xenophilius isn’t always exactly accurate, Dumbledore confirms this as true to Harry when they meet in King’s Cross, and further mentioned that Grindelwald sought out Ignotus’s grave in his quest for the Deathly Hallows.

In Beedle’s tale, they’re never named.

Though the three brothers are based off of the Peverells, they’re never actually named in “The Tale of the Three Brothers”. Individually, they’re referred to either by birth order or by a corresponding number - the oldest is also called the first.

“And then Death asked the third and youngest brother what he would like. The youngest brother was the humblest and also the wisest of the brothers, and he did not trust Death.”
_{^{- The Tales of Beedle the Bard}}

Collectively, they’re called the three brothers.

“Then Death stood aside and allowed the three brothers to continue on their way, and they did so, talking with wonder of the adventure they had had, and admiring Deaths gifts.”
_{^{- The Tales of Beedle the Bard}}

In Beedle’s story, like in many other fairy tales, the characters aren’t actually given names at any point in the story.

The Three Brothers who supposedly made a deal with Death were Antioch, Cadmus and Ignotus Peverell, ancestors of the Potter and Gaunt families, and the original owners of the Deathly Hallows. Dumbledore speculated that rather than dealing with Death they simply created the Hallows.

Whether they met Death on a lonely road . . . I think it more likely that the Peverell brothers were simply gifted, dangerous wizards who succeeded in creating those powerful objects. The story of them being Death’s own Hallows seems to me the sort of legend that might have sprung up around such creations.

Antioch, Cadmus and Ignotus.

We don't know how they got the Hallows but we do know for certain that it was these three brothers who were in the story.

Three legendary objects owned and likely created by the Peverell brothers. Together, they are said to make one 'master of death'
_{- The Deathly Hallows - Pottermore}

Another fun fact about these brothers is that they were the ancestors of the Gaunt and Potter families.

The stone and the cloak were passed down through the Gaunt and Potter families. The Elder Wand has changed hands many times, often through murderous means
_{- The Deathly Hallows - Pottermore}

And throughout the generations the cloak was passed down from parents to offspring.

In the Muggle world ‘Potter’ is an occupational surname, meaning a man who creates pottery. The wizarding family of Potters descends from the twelfth-century wizard Linfred of Stinchcombe, a locally well-beloved and eccentric man, whose nickname, ‘the Potterer’, became corrupted in time to ‘Potter’. Linfred was a vague and absent-minded fellow whose Muggle neighbours often called upon his medicinal services. None of them realised that Linfred’s wonderful cures for pox and ague were magical; they all thought him a harmless and lovable old chap, pottering about in his garden with all his funny plants. His reputation as a well-meaning eccentric served Linfred well, for behind closed doors he was able to continue the series of experiments that laid the foundation of the Potter family’s fortune. Historians credit Linfred as the originator of a number of remedies that evolved into potions still used to this day, including Skele-gro and Pepperup Potion. His sales of such cures to fellow witches and wizards enabled him to leave a significant pile of gold to each of his seven children upon his death.

Linfred’s eldest son, Hardwin, married a beautiful young witch by the name of Iolanthe Peverell, who came from the village of Godric’s Hollow. She was the granddaughter of Ignotus Peverell. In the absence of male heirs, she, the eldest of her generation, had inherited her grandfather’s invisibility cloak. It was, Iolanthe explained to Hardwin, a tradition in her family that the possession of this cloak remained a secret, and her new husband respected her wishes. From this time on, the cloak was handed down to the eldest in each new generation.
_{- The Potter Family - Pottermore}

Here's a shorter quote about the Gaunts.

Marvolo and his family were pure-blood descendants of Salazar Slytherin who lived on the outskirts of Little Hangleton. Despite living in squalor, he was immensely proud of two family heirlooms he had inherited: Slytherin’s locket and the Peverell ring. Marvolo was sent to Azkaban for injuring several Ministry officials. Upon his release six months later, he discovered that his daughter had run away to marry a Muggle.
_{- The Gaunt Family Tree - Pottermore}

It may have been that he stole it though... We can't be sure.