The Frost Giants are what I think of as the archetypical giants - they have a strong viking theme, they like raiding humanoids, they come in big viking longships to cause misery, and you can in general kill them without entering morally questionable areas. The
Frost Giant Everlasting One takes this theme to its logical conclusion, as we get a Frost Giant who is the strongest and most vicious of them all, mainly thanks to the corrupting influence of Vaprak, the Troll god.
The picture for the Everlasting One is pleasingly gnarly. The multitude of heads is handled pretty well, and the detail on the Giant’s equipment and arms is great and really ties into an anglo-saxon / norse aesthetic. It definitely looks deranged and mutated, something you’d not want to meet on the tundra.
The Everlasting Ones are basically the Frost Giants who, unable to rise up their might-focused Ordning alone, turn to the Troll God Vaprak, who makes them strong and regenerating. This means that the Everlasting One, given a substantial boost over their fellows by this blessing, can easily claim chieftian status over their tribe. But Vaprak is a fickle god, and his blessings can easily turn to mutation and obvious deformities, which will cause the tribe to eject the Everlasting One; it seems that worshipping Vaprak is a deeply Maug thing to do, and carries intense shame accordingly.
In Ancient Greek and Roman religious, the shame and criminality of one person could be felt to bring moral pollution to the community. The decision to drive someone out, and require them to seek atonement from the Gods by means of difficult pilgrimages and whatnot, was based on a desire to limit a community’s exposure to that pollution, and to expunge that already accrued. In other words, having a murderer in your midst was actually negative for everyone in the eyes of the gods. When I read of these Maug Frost Giants being cast out, that is what I think of; the pollution that comes upon the tribe. There is definitely some room to work with these ideas, for example with the players having to interact with a suddenly hyperactive tribe of Frost Giants who are trying to expunge their communal shame by feats of strength and warfare - a situation that can only be resolved by hunting down and eliminating the Everlasting One who started it all.
The Everlasting One can be used as a boss upgrade for a normal Frost Giant encounter, but I think that your players might be a touch confused by the fact that suddenly a Frost Giant is regenerating HP loss and growing heads and whatnot; you’d want to telegraph it somehow. They can also serve as lone encounters, or as the centre of a debased cult to Vaprak, populated by some of these, some Trolls, and some mutated Humanoids (like Grimlocks, which have a cannibalistic theme as well). I think that there is a lot of room to use them, but other than the Vaprak cult they are not going to be hugely different from a normal Frost Giant to your players, unless you really delve deep into the Maug and Mott concepts, taking a social approach to a not-very-social group of Giants.
The combat stats for the Everlasting One are brutally simple: it is an upgraded Frost Giant that can do extra damage and be resistant to enemy damage by using a barbarian
Rage ability, and it can regenerate 10hp a round if not affected by Fire or Acid. That makes them quite susceptible to Remorhages, now that I think about it, but otherwise I guess those damage types are rare among winter themed monsters. Interestingly, the extra heads here seems to be the same as for the Ettin - granting advantage on certain skills and saving throws - suggesting that this trait has been made deliberately standard across the game. I don’t remember if the DMG has it listed on the big racial abilities table. The Everlasting One works exactly like a normal Frost Giant otherwise, so you won’t have any complications to worry about.
Final opinion: a solid and interesting Giant variant, but one that will benefit from being separated out from its Frost Giant fellows in some way. The strength of the Giant chassis shows here, where relatively minor changes make a very scary looking opponent indeed.