You can. I think what you are thinking of you cannot use two weapons of the same name to fulfill a set bonus UNLESS they at least one of them is a relic or legendary.
From the DMG (pg. 14): THIS MIGHT NOT BE PAGE 14 anymore.
Set Bonuses & Duplicate Weapons
If both the weapons being wielded are part of the same set and are either Relics (blue title with a ***** near the bottom) or Legendaries (orange title and backing), they count as two items toward fulfilling that set’s quota. E.g., when trying to qualify for the Viper Strike set bonus, a monk could wield two +3 VIPER STRIKE FANGS (Relics) and wear one other Viper Strike item to qualify for the Viper Strike set bonus. Similarly, a ranger could wield two ASHER’S +5 VIPER STRIKE FANGS and they would count as two items toward the Viper Strike set. Wielding two +2 VIPER STRIKE FANGs (Ultra Rares) would only count as a single item toward the set’s quota because neither of those are Relics or Legendaries.
A character capable of wielding two weapons may wield two weapons with the same name regardless of rarity, but they only count as two items toward fulfilling a set bonus if both are either Relics or Legendaries. Putting it another way, wielding two same-named Common, Uncommon, Rare, Ultra Rare, Enhanced (***), or Exalted (****) weapons only count as a single item toward qualifying for a set bonus, but wielding two same-named Relic (*****) or Legendary weapons counts as two items toward the set.
Different-named set-piece weapons count as two items toward the set’s quota, regardless of rarity.
Note: Other than weapons and RUNESTONE FITTING BASEs, no character may equip more than one item of the same name—no matter what rarity the items are.
You either discover a star or you don't. You arrogant punk.