I don't think UNIX was ever meant to be single-user. This interview suggests that's not where the name came from anyway: https://www.linuxjournal.com/article/7035
If you think about it, much of the complexity of Multics come from its multi-user requirement with overly complex access control matrix, multitude of file types including design for multi-user support, etc. Thus the Unix name metaphor or pun is to make it the latter simple by requirement and design. Remember that Unix was started as a skunkwork and even the original PDP-7 that being used originally was donated by other department of AT&T if I remember correctly it was the sound signal processing department [1]. If it is an official project, the multi-user requirement will be there from the start since arguably AT&T is the largest technical company at the time and they will want multi-user from the get-go.
But after some time and considerable success of Unix, the designers probably looks childish due to the naming since they did introduce multi-user at the later stage, and toned down the exact meaning of Unix. What is the opposite of multi, it is uni.
[1] The Strange Birth and Long Life of Unix:
https://spectrum.ieee.org/the-strange-birth-and-long-life-of...
> Because the new operating system supported only one user (Thompson), he saw it as ...
This has a lot more good references too: https://retrocomputing.stackexchange.com/questions/10907/was...
[1] Unix: