Says Jimmy Maher, who should know, On-Line Systems was "a name fairly typical of the vaguely futuristic, vaguely compound, but essentially meaningless names (Microsoft, anyone?) that were so common in the era." https://www.filfre.net/2011/10/ken-and-roberta/

This plausible explanation might not have anything to do with the actual reason for the name...

Computer scientists still refer to "online algorithms" as meaning "algorithms which process each input as it comes in". The obvious algorithm for "find the minimum element" is online for example, since you can stop at any point and say what the smallest you've seen so far is; however finding the median takes more work (you need to maintain two heaps, vs. simply collecting all the data and sorting it at the end).