In science we attempt to classify everything. And everything seems to be a subset of something else. Planet is a part of a solar system, solar system is a part of a galaxy, galaxy is part of the universe, universe is a part of our dimension, etc.
Obviously there are exceptions to this, rogue planets, but we still consider them contained.
I understand the idea of multidimensions is theoretical, but if they exist, do we have a name or even a theory what might contain them?
Maybe this was already said, but to be clear, they do not have to be in anything. There are a lot of theories regarding universe, multiverse, and stuff, but this is separate from dimensions of our universe and of those being in anything as far as I know.
As far as dimensions I think is is more about how they relate to each other, what shape they have, and to what extent we have access them, etc.