Axolotlia is clearly named after the axolotl, the Mexican salamander. However, a few axolotls arrived to the islands in 1743. The settlers in the British Colony of Atlantis (The name of Axolotlia while a British colony) named the lake after the axolotls and nicknamed the capital of the colony “Axoton” (formerly Elizabethtown). When the colony of Atlantis gained independence in 1974, axolotls made up such a huge part of its identity, it named itself the Republic of Axolotlia (because the islands were never a part of Atlantis after all, never related to Atlantis in any way).
You will notice that The Colony of Atlantis will rebel against the British multiple times, only being successful twice, the first time is short, strong, and only de facto, the second time is what made the modern Republic of Axolotlia as we know it.