So, Halbrand would hold a grudge if he is Sauron and Adar had tried to kill him (and perhaps severely injured him), but now Sauron has taken the form of Halbrand, then Adar would not recognise him.
The implication of that question "do you remember me" is that they obviously met but Halbrand's appearance wouldn't be recognizable by Adar. Because in appearance Sauron is different than Halbrand, the latter is just a disguise.
Halbrand refused to reveal his true identity to Adar
He served under Morgoth and claims that he killed Sauron. He does not seem to recognize Halbrand as Sauron, and yet he carries out what we can assume is his master's evil bidding by setting in motion the events that burn the Southlands and create Mordor.
Adar also claimed to have killed Sauron after watching Sauron experiment on the orcs, whom Adar sees as his children. It's possible Adar was pretending not to recognize Sauron as part of a ruse. But Adar also may truly think he did kill Sauron, but he failed and now the dark lord has returned in a disguise.
Rather than killing a loved one, therefore, maybe Halbrand seeks revenge because Adar killed him, and "chased me from my homeland" referred to this betrayal.
Even Halbrand asking Adar if he remembers him makes sense in the context of his being Sauron. First. Halbrand would be testing the veracity of his own disguise. If Adar, who served with and for Sauron in the First Age, can't recognize him as Halbrand, no one can.
In fact, Adar believes he killed Sauron. The one-time elf was doing it for his orc children whom he loves, many of whom Sauron had sacrificed in his quest to rule Middle-earth.
Adar revealed his entire story to Galadriel, and what he told her will change her mission in the Second Age. Adar is an original Orc, and he served Morgoth and Sauron. His life has been one of darkness, but his attack on the Southlands is a desperate attempt to create a home for his offspring.
There's a small chance that Adar actually did attack Sauron, banishing him from his physical form and causing him to exist only in spirit. There are other important events in Tolkien lore, though, that are tied both to this show's plot and the different forms Sauron has embodied.
There have been consistent reports he is a fallen Elf, a quite dramatic departure from Tolkien's own lore given he moved away from the idea that Elves can fall to the Shadow.
A mysterious individual of the Second Age was referred to as Adar, or "Lord-father", by Orcs, presumably because, according to Galadriel, of his status as one of the Moriondor, the first Elves to be captured and tortured by Morgoth.
As for whether Halbrand actually loved or romantically desired Galadriel is to be determined. Sauron is an expert manipulator and likely sees Galadriel and her power as an asset. In line with the old adage, "Keep your friends close; keep your enemies closer," he'd rather have her on his side than against him.
When Galadriel calls Adar's kind — captured Elves tortured and twisted into becoming Morgoth's evil minions — “Moriondor,” which translates to “sons of the dark” in Elvish, Adar says he prefers the term “Uruk,” which is the word for “Orc” in the Black Speech of Mordor.
According to Galadriel, when the Elves first awoke at the beginning of the First Age, Adar was possibly one of many of them who were taken by Morgoth. He was tortured and twisted, becoming one of the first Orcs, a new and ruinous form of life.
Historyedit edit source. Halbrand was once the supposed King of the Southlands before Orcs drove him out alongside many others. Halbrand fled with them onto a ship sailing through the Sundering Seas.
Why did Halbrand stop Galadriel from killing Adar?
The dark elf, or Uruk, does not recall Halbrand who prepares to kill Adar until Galadriel talks him out of it. Halbrand comments that Galadriel doesn't know what Adar did, to which the Uruk asks if he caused pain to someone Halbrand loved - suggesting it was a woman or a child.
Adar, therefore, seems to honestly believe he killed the Dark Lord. He's almost certainly mistaken. Sauron is one of the Maiar - angelic and immortal spirits from the beginning of time. Since the Maiar are divine, primordial beings, they don't die in the traditional sense.
At some point prior to The Rings of Power, Sauron conjured a fresh physical form. He then seized the Southlands' crest from its last known king (who died 1000 years prior to the TV show's timeline) and assumed the identity "Halbrand."
Elrond discovered the scroll that revealed that Halbrand couldn't be King of the Southlanders, so it's likely that he realized that Halbrand was Sauron and that he escaped. Knowing that Sauron is on the loose, he could warn the dwarves of the growing evil and encourage them to forge their own rings.
When exactly did Galadriel start to suspect that her traveling companion is not who he says he is? Clark said it was one particular moment in The Rings of Power finale. "When Celebrimbor (Charles Edwards) mentions 'the power over flesh,' and she's only ever heard Adar (Joseph Mawle) mention that before," Clark said.
Adar soon became disillusioned with the Dark Lord and disgusted by the selfish sacrificing of his "children" for dabblings in the Unseen World. Having had enough of slavery, Adar broke his shackles to Sauron and turned on him, going as far as to slay him.
According to Polygon, Sauron was building up his forces in Mordor, which is close to the Southlands. All signs point to Adar not being Sauron, though. During the Second Age, he used his shapeshifting ability to appear as the friendly Annatar so he could learn ringcraft.
