Okey doke. Naming conventions for chapters vary between fraternity/sorority and if there are different types of chapters in the same org (e.g. collegiate/alumni then those may also have different naming methods).
Take for example a social (i.e. generally non co-ed) fraternity: it would usually term it's
first ever chapter as the Alpha chapter, then Beta chapter and so forth. And they go through the Greek alphabet as new chapters are added; some fraternities use two names in title e.g. Beta Gamma chapter of XYZ fraternity. I
believe most groups use single greek letters until they reach the end of the Greek alphabet then move to multiple words in the chapter name. So, an established fraternity from the 19th century installing new chapters with multiple lettered names might have some of its chapters with single letters still around and some might've closed down over the years.
Also, sometimes when a chapter exists at a university but closes down and say a few years later recolonises ('comes back') the national fraternity may give the exact same name as before or some groups (like Alpha Phi womens sorority - which is called a fraternity technically) rename it with the word "Deuteron" to indicate it's returned and is the second time around. E.g. Beta Nu Deuteron chapter of Alpha Phi at Duke's university.
Or...
then you have lots of fraternities like Phi Psi who use the state name as part of the chapter designation:
e.g. Pennsylvania Epsilon chapter at Gettysburg College.
Or... some professional (or other) fraternities might simply either name their group after the university -
SuchandSuch_university chapter of XYZ fraternity or after a famous person in that professional field e.g the
Benton chapter of Phi Alpha Delta Law Fraternity at University of Missouri.
There will tend to be some variation from group to group with no hard and fast rules as to what they use but I believe the alphabetical letters in sequence then multiple greek letters is the most common method. Hope that gives an idea, other members on the board shall probably give more details or correct any mistakes I may've made.
ETA: A very quick look at AKpsi's website shows they appear to use some alphabetical sequence, having a Beta chapter as well as, say, a Delta Zeta chapter.
Also, you may already know it but just in case here's a
link to a webpage created by a member on this site. giving the greek alphabet with a picture of the letter and pronunciation.