Human Designations Alpha Halo and Delta Halo. Alpha halo is the first halo ring found by humans, Delta halo the 2nd since Greek designations are used and likely chosen by the AI cortona or whatever AI is the first finder of said halo ring... *there is quite a bit of Greek, and Roman mythology to be found in the halo universe actually. So it would stand to reason that the others if found would be given such monikers, The Ark as you know refers to the machine outside of the milky way *and the influence of the rings firing and the flood* and the story of Noah and the ark.
NOTE:The Ark was not named such by humans but by the forerunners, The halo rings are not refered to by the greek alphabet by the monitors or the forerunners....
Greek letters are as follows... though there would be a limit and there is no Greek letter describing the Ark and there are 7 count em 7 halo rings including the destroyed halo ring which *spoiler* was recreated by the ark in halo 3.
As referred to by The AI monitors of the rings. The Monitors refer to them as installations with regular numeric monikers.
The Ark-Installation 00
Alpha halo-Installation 04
Delta Halo-Installation 05
This is logical since they are supremely logical machines with next to no emotional response when created except that which they developed over the millenia of being on the rings *and often psychotic personality types*
Names as known by the Covenant. There is only one know and that's the Sacred rings.
Names Known to the Forerunners. Fortress worlds, all of them are known as The Array.
As per the Greek Alphabet if we follow the Installation numbers.
00-07
the Ark would have no Greek equivalent because i do not believe there is an alpha numeric for 0 in the Greek alphabet BUT the word Zero descends from the Greek word Zephyrus.
The rest are as follows.
Alpha,Beta,Gamma,Delta,Epsilon,Zeta,Eta. Kappa is in there from what I've been reading on the rings since i wrote this up though i dont know why if their are 7 rings then the end would be ETA, if kappa is used then theta and Iota are ignored.