The moves are the vehicles of Pokemon battles; they're what keeps the battles going. Just as they do with Pokemon, features, and abilities, Game Freak comes up with a new set of moves every generation with each being useful in its own way. Said moves vary in type, quality, and availability, so naturally some of them will stand out more than others.
Generation VIII has introduced particularly many new moves both from the base Sword and Shield games and the subsequent DLCs. Many of them had wholly unique properties not seen in previous generations, thus gaining viability in both offline playthroughs and online competitive battling.
Note: This list will include moves from The Isle of Armor and The Crown Tundra DLCs, but not Max or G-Max moves.
10 Fishous Rend
The signature move of Dracovish and Arctovish, this move has made the former incredibly powerful and even gotten it banned to Smogon's Uber tier despite its underwhelming stats.
Fishous Rend is an 85 base power physical Water-type move that is twice as powerful when the user goes first. All those properties fit well with Dracovish in particular, with its STAB Water-typing, a boost from its ability Strong Jaw, and the typical competitive setup of using it in the rain while holding a Choice Scarf or Band. It learns the move by level-up at level 63 which will take a while, but once it gets there, it can easily mow through its competition.
9 Pyro Ball
Pyro Ball is Cinderace's signature attacking move, and it's pretty straightforward. It sports a massive 120 base power which is quite high for a STAB move you can spam over and over -- especially with Cinderace's high physical Attack and Speed stats. It also has a bonus 10% chance to burn its target.
It does have a few minor fallbacks: a 90% accuracy which isn't terrible but will hurt to miss, being a "bullet" move that's not affected by Pokemon with the Bulletproof ability, and a guarantee to thaw out frozen Pokemon when it hits. Aside from its viability, it's become an incredibly popular move for having one of the only cool-looking move animations in Sword and Shield. This reinforces the Fire-type starter's gimmick as a football player.
8 Shell Side Arm
The Isle of Armor introduced Galarian Slowbro and with it, many of its signature capabilities including its ability Quick Draw and its signature move -- Shell Side Arm. This move, in many respects, is a run-of-the-mill competitive attacking move that deals 90 base power Poison-type damage.
What makes it special (or...physical?) is its ability to switch between physical and special damage depending on what will be more powerful for its target. That matches well with Galarian Slowbro having both Attack and Special Attack equally at 100, making it formidable on the offensive end no matter the kind of damage it will deal. Pokemon that are only walls on either the physical or special side will take big damage from this move either way.
7 Grassy Glide
This is the first move on this list not to be a signature as it was introduced as an Isle of Armor tutor move. It might as well be an honorary one though since it is most closely associated with Rillaboom. Its natural properties work perfectly in tandem with the Grass-type starter's hidden ability, Grassy Surge.
Grassy Glide is a 70 base power physical Grass-type move that gains one level of priority in Grassy Terrain along with the standard 30% power boost to Grass-type moves. Its synergy with Rillaboom's stat spread as a physical attacker that could use a bit more speed makes it more viable than Rillaboom's actual signature move, Drum Beating, which is OK at best.
6 Court Change
Game Freak gave Cinderace so much love that it has two signature moves: the aforementioned Pyro Ball and one of the most unique utility moves ever, Court Change. Court Change is a status move that switches side-specific in-field effects such as barriers, entry hazards, and the like from the user's side over to the target's, and vice versa.
No other move like that has existed in the franchise and has given Cinderace a bit more value in the Generation VIII metagame along with its other qualities. If anything, it has made such effects a bit less viable with competitive singles battlers being warier of Cinderace's ability to have its opponent be negatively affected by its own hazards.
5 No Retreat
Another weird signature move, No Retreat calls Falinks as its signature user and it works just as its name implies. It's another status move as it has the interesting but possibly detrimental effects of giving the user a one-stage omni-boost (i.e. a boost to every possible stat except accuracy and evasion), but traps said user from switching out.
In a vacuum, it's an incredible move. It even fits Falinks' concept as a Pokemon, but it can be risky to use -- especially since the little line of soldiers have bad stats and an exploitable defensive type. Still, if players can set this move up correctly, Falinks could potentially sweep opposing teams.
4 Flip Turn
This is another Isle of Armor tutor move and it's seen the most widespread competitive use out of all of them. Flip Turn deals 60 base power physical damage and, upon so, switches the user out for a teammate of the player's choosing. Much has been said about moves like Flip Turn, U-Turn, and Volt Switch, due to their usefulness in gaining momentum in competitive battles.
Flip Turn, in particular, has become a staple on many Water-type Pokemon's movesets -- especially on Swift Swim rain sweepers like Barraskewda and Kingdra who gain both STAB and a boost from the rain. It's also most notably breathed new competitive life into Swampert, giving it viability as a bulky scout after it lost its Mega Evolution.
3 Wicked Blow & Surging Strikes
Isle of Armor mascot Urshifu gains either of two signature moves depending on the style it evolves into: Wicked Blow for the Single Strike Style variant or Surging Strikes for Rapid Strike Style. Both have the same gimmick of being guaranteed critical hits, therefore giving Urshifu much viability as a wallbreaker. It syncs up especially well with its Unseen Fist ability that allows either move to attack through Protect.
What differentiates the two moves besides their types are the base power and number of hits. Wicked Blow is a Dark-type 80 base power one-hit move while Surging Strikes is a Water-type 25 base power three-hit move. Neither is much more viable than the other, though Surging Strikes being a multi-hit move can help deal damage while breaking Substitutes and the like (e.g. Mimikyu's Disguise).
2 Glacial Lance & Astral Barrage
These two moves are another pair of form-exclusive signature moves for a DLC mascot -- this time for The Crown Tundra's Calyrex. Ice Rider Calyrex, formed after fusing with Glastrier, learns the physical Ice-type move, Glacial Lance. In contrast, Shadow Rider Calyrex, after its fusion with Spectrier, learns the special Ghost-type move Astral Barrage. Both are straightforward, no-frills, powerful attacks at 130 and 120 base power respectively.
While there really isn't much to differentiate the two besides type and category, the differences in the two forms are quite stark. Shadow Rider arguably has a better stat spread with more focus as a special sweeper while Ice Rider is a defensive tank to go along with physical attacking power. Shadow Rider is easier to use, but Ice Rider could work very well in tandem with Trick Room.
1 Behemoth Blade, Behemoth Bash, & Dynamax Cannon
Rounding out the list and the signature moves of game mascots, the base game's box mascots get their shine with their exclusive moves: Zacian's Behemoth Blade and Zamazenta's Behemoth Bash. They are essentially the same move with 100 base power, physical damage, and Steel-typing. Moreover, they have the added effect of doubling base power on a Dynamaxed target.
Both are obtained by giving each Legendary their respective held item while knowing Iron Head: the Rusted Sword for Zacian and the Rusted Shield for Zamazenta. A notable variant of this move is Dynamax Cannon: Eternatus' signature move. It holds the same effects and base power, though it is now a special Dragon-type move. All three members of this Legendary trio have been banned to Ubers due, in large part, to their respective signature moves that help in eliminating Dynamaxed opponents.