You are right unless we define 'universe' as everything that is. Then what we have until now thought of as the universe is just a sub-component of the actual universe and it needs a different name.
Of course the more the definition of 'universe' is stretched the less it means. If we add 'everything that was' and 'everything that will be' to 'everything that is' to the definition of 'universe' it becomes less and less quantifiable. Add 'everything that never was and never will be' (why not? isn't the universe 'everything?') and 'universe' becomes something that is impossible to ever measure, mentally picture or understand.
I simultaneously love and hate these mental conundrums. ;^)
To me just the word “uni” designates an individual thing.