Main or Special trios
Weather Trio
The weather trio is a fan term applied to the three ancient Legendary Pokémon from Hoenn legend—Groudon, Kyogre, and Rayquaza. In the games, they are referred to as the super-ancient Pokémon (Japanese: 超古代ポケモン super-ancient Pokémon), and another fan nickname is "elemental trio".
Source
Creation Trio
The subject of this article has no official name.
The name currently in use is a fan designator; see below for more information.
The creation trio is a fan term used to refer to three powerful Legendary Pokémon of the Sinnoh region: Dialga, Palkia, and Giratina. Other fan terms include deity trio and dragon trio.
Source
Tao Trio
The subject of this article has no official name.
The name currently in use is a fan designator; see below for more information.
The Tao trio is a collective fan term used to refer to the three powerful Legendary Pokémon of the Unova Region: Reshiram, Zekrom, and Kyurem. Other fan terms include Tao dragon trio and energy trio.
Source
Aura Trio
The subject of this article has no official name.
The name currently in use is a fan designator; see below for more information.
Aura trio is a fan term for the legendary trio of Kalos, consisting of Xerneas, Yveltal, and Zygarde, the first two of which are found at the Team Flare Secret HQ in Pokémon X and Y, respectively.
Source
Light Trio
The subject of this article has no official name.
The name currently in use is a fan designator; see below for more information.
Light trio is a fan term for the Legendary trio of Alola that consists of Solgaleo, Lunala, and Necrozma.
Source
Other Legendary Trios
Legendary Birds
Legendary birds (Japanese: 伝説の鳥ポケモン Legendary bird Pokémon) is a collective term used to refer to the trio of Articuno, Zapdos, and Moltres. They are also known as the winged mirages (Japanese: 幻の翼 phantom wings). In the Crown Tundra, their Galarian versions have been referred to as legendary wings.
Source
Legendary Beasts
Legendary beasts (Japanese: 伝説の獣ポケモン Legendary beast Pokémon) is a collective term used to refer to the trio of Raikou, Entei and Suicune.
Source
Lake Guardians
The lake guardians (Japanese: 湖の神々 lake gods), or lake trio, is a term used to describe the Legendary trio residing in the three lakes of Sinnoh: Uxie, Mesprit, and Azelf.
Forces of Nature
The Forces of Nature (Japanese: 大自然の力 forces of nature) is a collective term to refer to the all-male Legendary trio of Tornadus, Thundurus, and Landorus. They are also known by fans as the kami trio, cloud trio, or Legendary genies.
Source
As such, we can tell that the important or main/special trios all have fan terms while "other legendary trios" have been referred by that name in anime or shown in games.
Duos
Tower duo
The tower duo is a fan term for the Legendary duo of Johto that consists of Lugia and Ho-Oh. Lugia and Ho-Oh are often regarded as polar opposites.
Source
Eon duo
The eon duo is a fan term for a Legendary duo of Hoenn that consists of Latias and Latios, which are also that region's roaming Pokémon.
Source
Lunar Duo
The lunar duo is a fan term for a duo of Sinnoh that consists of the Legendary Cresselia and the Mythical Darkrai.
Source
Hero duo
The hero duo is a fan term to describe the main legendary duo of Galar, consisting of Zacian and Zamazenta.
Source
So, all of these duos name are fan term.
Hope this helps. Comment if anything missing.