The word we use to refer to what's inside the cosmic horizon is the 'universe', so what would you call the empty space outside of the horizon?
Since the universe is expanding, the things (galaxies, quasars, etc) that are currently in the observable region, on our side of the cosmic horizon, will someday be over the horizon. It stands to reason, then, that whatever is currently over the horizon is just the things that were once on our side, but long ago.
This relates to what I was saying about the universe was once the size of a grapefruit morphing into the observable universe was once the size of a grapefruit. Along with the universe is infinite. IMHO there is no evidence for the latter.
To be pedantic, I guess the answer to your question is "the non-observable universe". That’s because the word universe is derived from “uni” as in unicycle and “verse” as in vice versa. It means turned into one. It means everything. Hence the word "multiverse" doesn't float my boat.