Om Sauron var Morgoths mest betrodda löjtnant, varför tog alla sina ringar?

Eftersom de inte visste att han var Sauron .

Från Rings of Power och Tredjeården :

Of old there was Sauron the Maia, whom the Sindar in Beleriand named Gorthaur. In the beginning of Arda Melkor seduced him to his allegiance, and he became the greatest and most trusted of the servants of the Enemy, and the most perilous, for he could assume many forms, and for long if he willed he could still appear noble and beautiful, so as to deceive all but the most wary.

Han var ganska framgångsrik i denna bedrägeri, och endast Elrond och Gil-galad togs inte in av honom.

... long he sought to persuade the Elves to his service, for he knew that the Firstborn had the greater power; and he went far and wide among them, and his hue was still that of one both fair and wise. Only to Lindon he did not come, for Gil-galad and Elrond doubted him and his fair-seeming, and though they knew not who in truth he was they would not admit him to that land. But elsewhere the Elves received him gladly, and few among them hearkened to the messengers from Lindon bidding them beware; for Sauron took to himself the name of Annatar, the Lord of Gifts, and they had at first much profit from his friendship.

Annanstans (i ofärdiga talar), och som karaktären av Galadriel utvecklades, berättas att hon också inte avkunnades och var faktiskt hans främsta motståndare:

In Eregion Sauron posed as an emissary of the Valar, sent by them to Middle-earth ("thus anticipating the Istari") or ordered by them to remain there to give aid to the Elves. He perceived at once that Galadriel would be his chief adversary and obstacle, and he endeavoured therefore to placate her, bearing her scorn with outward patience and courtesy.

Anledningen ges i en fotnot till texten enligt följande:

The note goes on to say that Galadriel was not deceived, saying that this Aulendil was not in the train of Aulë in Valinor, "but this is not decisive, since Aulë existed before the 'Building of Arda,' and the probability is that Sauron was in fact one of the Aulëan Maiar, corrupted 'before Arda began' by Melkor."

Trots allt var han väldigt framgångsrik när han dömde den andra Noldor:

Sauron used all his arts upon Celebrimbor and his fellow-smiths, who had formed a society or brotherhood, very powerful in Eregion, the Gwaith-i-Mírdain; but he worked in secret, unknown to Galadriel and Celeborn. Before long Sauron had the Gwaith-iMírdain under his influence, for at first they had great profit from his instruction in secret matters of their craft.

Vad som är särskilt ironiskt om detta är att det är exakt samma svaghet i Noldor som Melkor hade utnyttjat när han avkunnade dem i Valinor, som Silmarillion berättar:

But the Noldor took delight in the hidden knowledge that he could reveal to them; and some hearkened to words that it would have been better for them never to have heard.

Således öppnade han inte sig själv som Sauron men hävdade att han var någon annan, i vissa versioner av berättelserna en ambassadör från Valaren, och det var först efter att han hade smidd den One Ring som älvorna visste att de hade varit decieved; igen från Rings of Power :

As soon as Sauron set the One Ring upon his finger they were aware of him; and they knew him, and perceived that he would be master of them, and of all that they wrought.

Det finns ett felaktigt uttalande i din fråga - att Sauron hade skapat Rings of Power. Det gjorde han faktiskt inte; Den enda Ring som Sauron skapade var den ena . Älven skapade de andra ringarna men med hjälp av hans instruktioner; igen från Rings of Power :

In those days the smiths of Ost-in-Edhil surpassed all that they had contrived before; and they took thought, and they made Rings of Power. But Sauron guided their labours, and he was aware of all that they did...

Now the Elves made many rings; but secretly Sauron made One Ring to rule all the others, and their power was bound up with it, to be subject wholly to it and to last only so long as it too should last.

Seven Rings he gave to the Dwarves; but to Men he gave nine, for Men proved in this matter as in others the readiest to his will.

The Dwarves indeed proved tough and hard to tame; they ill endure the domination of others, and the thoughts of their hearts are hard to fathom, nor can they be turned to shadows. They used their rings only for the getting of wealth; but wrath and an over-mastering greed of gold were kindled in their hearts, of which evil enough after came to the profit of Sauron.

Men proved easier to ensnare. Those who used the Nine Rings became mighty in their day, kings, sorcerers, and warriors of old. They obtained glory and great wealth...

Även om det inte uttryckligen anges, förefaller det rimligt att anta att män och dvärgar också skulle ha haft lite mindre kunskaper om exakt vem de hade att göra med.