Not sure there is a hard and fast answer--specific traditions might be able to tell "for sure" about a specific kata in their tradition.
What I have been told--which may or may not be wholly accurate.
1-As you suggested some of the kata--the Heian/Pinan series comes to mind as "some" of them are reputedly a single kata that was broken into several kata for some purpose way back in the day.
Oddly enough I have heard the same about the tekkei/Nihanchi series as well.
2-Some of the them are "supposed" to because they were done that way by different, highly skilled/important people in the early days of the art. As in "master x does it a bit differently because he focused on X, or he was large and strong or small and fast. So the 2 kata reflect the personal applications of a specific person.
That may or may not be the truth--while true many experts perform the same kata somewhat differently the tendency is often to "standardize" the kata for given style. SO whatever personal "signatures" might have been present at one time may no longer be there.
2b-Also might be a "hold over" kata that someone back in the day learned from a "sister" style. As sort of "this is how they do it over in Tomari" kind of thing and over time it kinda stuck in the system.
3-Somebody, somewhere, sometime, might have thought a given kata was "too difficult" and broke it into 2 sections--the "easier" one and its "harder" section.
4-Somebody might have noticed that their particular system has "too few" kata and they thought the students might be getting bored--IMO system tend to gain kata and techniques over time. So they simply split them up or "adapted" a given kata.
4B-Also possible that some were "split up" to focus on a specific application---then you get into the bunkai/pick your term here
of the application of the kata.
5-Could be that names have simply become lost--most of the traditional arts have been around a long time--maybe somebody could not recall what the name of some kata was so they simple stuck a NUMBER with it. Has similar or complmentary techniques so its now "Dai Ichi."
5B-Seriously, it could just be a matter of some "inside" name that everybody in the group called it so it stuck--I know living people that have been called by their nicknames so long its how EVERYBODY refers to them now---they have actual given names of course--just everybody they know uses the nickname---if it can happen to people it can happen to things. Wouldn't take very long to have everyone in a given group to start calling a kata "X" and it sticking.
6-Some of the are almost certainly listed that way because they they were desigend and created that way. It was intentional.
7-Some of the Goju kata translate to numbers--its been a question for many years with some Goju folks if the numbers ARE the actual direct translations from the Chinese. If the number are some form of "shorthand" from much longer and more creative names like "13 dragons fighting the tiger"
and the Okinawans just called "13." Or if somebody that really didn't care WHAT you called it--they were just interested how you apply/use it just USED numbers instead.
Many/most people don't really get interested in the history and specific of their arts until later in their martial studies (ya--generalizing here) they want to study for self defense. Not all that different back in the day---by the time a student gets really/seriously interested in the minutia of the style their master is sometime dead or too far away to ask.
Not sure that many people would even ask "why is it called dai ichi/sho/dai and by the time they are good enough with the kata to care--it might well be too late to ask the person that knew.
How many stories could my grandfather have told me that I never thought to ask?
By the time I was actually interested--it was too late.
Sorry to be a downer here--just made me think about it. It might be just that simple....heck maybe THEIR teacher didn't ask either--and now your living in Okinawa or you have moved to Japan and nobody asks you...............
8-Your guess is a good mine
Hope someone has a better idea/s than I do.