There's a general problem with mathematics that every researcher eventually encounters. There aren't enough letters in the alphabet.
In probability (the only discipline I research) if you discover a new distribution then most of the time one of two things has happened.
1.$\qquad$You've proposed an exotic or special formula at the beginning of your paper so you give it an exotic name, like a Greek letter.
2.$\qquad$You've spent ten pages deriving the formula for your distribution and you've run out of normal letters.
So some of the time the new distributions get given Greek letters. Not always true, the $T$ distribution is important, $W$ is usually used for Brownian motion which is more important than all the other distributions put together.
You might find a pattern that helps to remember them, but it will be a coincidence, not a rule.