Two egg or two eggs

Its not plural because they decided to name the town Two Egg.
Depending on the kind of shop you could do some word play with the Egg being plural. But if you just want the name of the town then Two Egg would be correct.

I think it's a kind of stable expression/phrasal verb and there's no spesicif reason why people called the city Two Egg, but you may cotnact locals and find out the reason if you want.

There is a practice among some English dialects of using a singular noun in measurements. For example, an English person might describe their weight as "10 stone." Perhaps it comes from the adjectival form, such as "I made a three-egg omelette," where the noun is never plural. As to your marketing question, pick the version that you think would stand out. How about "Too Egg"?