Here’s a list detailing the meanings of the Masters actual names, these names are allegedly taken from the Japanese guide book, but as I have never seen it for myself, I cannot confirm whether or not that's actually true. The first word is in relation to their number and (with the exception of the Wellspring Steeple Master whose number is written in Spanish) are written in Tigrinya for some unknown reason. Also, I should mention that some of the Tigrinya numbers may or may not be misspelled, I can't say for certain because the results I found online were inconsistent.
Master of the Treetop Tower: Hade Cyclops = No. 1 Cyclops: I imagine most people have heard of a Cyclops before, they are giant one-eyed creatures from Greek mythology. However, this name is rather misleading as the Master of the Treetop Tower clearly has a normal face with two eyes.
Master of the Sheerdrop Spire: Kilte Airāvata = No. 2 Airāvata: In Hinduism Airavata is a magical flying white elephant that serves as the steed for the god Indra. The Master of the Sheerdrop Spire actually does resemble an elephant, particularly its head which has a trunk, large elephant ears and tusks.
Master of the Wellspring Steeple: Tres Aegir = No. 3 Aegir: In Old Norse "Aegir" means "Sea" and in Norse mythology is the name of a sea jötunn (giant) associated with the ocean. This title is fitting seeing as the Master of the Wellspring Steeple is water themed.
Master of the Crimson Keep: Arba'ete Surtr = No. 4 Surtr: In Old Norse "Surtr" means "Black" and in Norse mythology Surtr is a jötunn who rules the realm of fire, Muspelheim. This one is pretty self-explanatory as the Master of the Crimson Keep is a fiery giant.
Master of the Ironclad Turret: Hamushte Jābir = No. 5 Jābir: I beleive that this Master's name is a reference to Jabir ibn Hayyan (also known as "Geber") a famous 8th-century alchemist who is widely credited as the Father of Chemistry. He theorized that by rearranging the qualities of a metal, a different metal could be produced. This would tie-in well with the Ironclad Turret as it is associated with the element of metal.
Master of the Arcadian Tower: Shidishte Shesha = No. 6 Shesha: In Hinduism Shesha is the king of all nagas (a race of half-human, half-serpent beings) and is one of the primal beings of creation. He is usually depicted as a massive coiled serpent with as many as five to one-thousand heads. The Master of the Arcadian Tower has a serpent-like body and it slithers around like a snake.
Master of the Rockshard Rampart: Shob'ate Serket = No. 7 Serket: Serket is a goddess from Egyptian mythology who is associated with scorpions. She is typically depicted as a woman with a scorpion on her head and occasionally as a scorpion with the head of a woman. The design for the Master of the Rockshard Rampart is clearly based on the latter description.
Master of the Torrent Peak: Shomonte nhr = No. 8 nhr: In some languages "nhr" (or "Nahar") means "river." This name is most likely referring to "Judge Nahar" a title of the Canaanite god of the sea, "Yam." From what I can find Yam is usually described as either a serpent or a dragon. Yam and the Master of the Torrent Peak are both accosted with water, but I don't see any similarities between the two in terms of appearance.
Master of the Blazing Citadel: Tishi'ate Miθra = No. 9 Miθra: Miθra, more commonly known as "Mithra" or "Mitra" is a yazata (a Zoroastrian divinity.) Mithra is the god of contracts and the protector of truth; he was also worshiped as a sun god.
Master of the Truegold Tower: Aserte Arcana = No. 10 Arcana: "Arcana" is the plural of Arcanum which means "profound secret." To the alchemists of the Middle Ages, the arcana was a supposed great secret of nature which they sought to discover. Truegold Tower's name and element (metal) are likely a reference to the most well-known goal of alchemists, trying to transmutation metals into gold.
Masters of the Blacklight Barbican: Aserte hade Rahu & Aserte kilte Ketu = No. 11 Rahu & No. 12 Ketu: In Hindu astrology Rahu and Ketu are the name given to the nodes of the moon. Rahu is the north node and Ketu is the south node. In Hinduism Visnu decided to make the deities (the planets) immortal by giving them a sacred nectar called "amrita." However a dragon-like Rakshasa (basically a demon or evil spirit in Hinduism) disguised itself as a deity in order to become immortal. Upon realizing that he had been fooled Vishnu decapitated the Rakshasa, but as he had already received the nectar he could no longer die. Instead his head became Rahu and his tail became Ketu.
Additionally, the Masters of the Blacklight Barbican's designs are clearly based on the concept of Yin and Yang from ancient Chinese philosophy. To put it simply, Yin and Yang are contrary, but complimentary energies that balance each other out. Yin is characterized as an inward energy that is feminine, dark and negative while Yang is characterized as outward energy, masculine, hot and positive. This is reflected with the Masters, Rahu and Ketu as Rahu has masculine features and is associated with light while Katu has feminine features and is associated with dark.
Zeron: Bado Shub-Niggurath = No. 0: Shub-Niggurath: Shub-Niggurath is a deity from the Cthulhu Mythos. The Cthulhu Mythos is a shared fictional universe, originating from the works of American horror writer H. P. Lovecraft. Shub-Niggurath is often associated with the epithet "The Black Goat of the Woods with a Thousand Young," however it's possible that the aforementioned "Black Goat" and "Shub-Niggurath" are actually separate entities. Her physcial apperance was never described by Lovecraft, but many artist depictions exist. Nonetheless, Zeron's final form does look a lot like something you'd expect to see in a Lovecraft story.