The consultant answer of "it depends" applies here. Assuming you are retiring and replacing the business schema because there have been significant changes, it may not be as easy as sliding the new schema in under the existing dashboard/insights.
That said, you can export the dashboard and open it in your favorite text editor ( e.g. Notepad++ ) and search/replace the schema name.
If you've changed column names you'd obviously need a map from original to new. ( name only, I don't think the label is used for anything other than creating the initial column heading text - happy to be corrected if that's not so ) and, of course, if you've retired one name and then reused it for something else it gets more complex.
Of course if the new Business Schema also relies on a new physical schema you'll need to take the same steps. Probably before any dashboard transition work so all the physical schema references work before you change the dashboard references.
Probably goes w/out saying, but export and keep copies of everything just in case things go sideways somewhere between start and finish!