Depending on the changes made to your Google My Business listing, you may be able to move your reviews. This usually applies to businesses that have moved. If your business moves from one location to another within the same city or a neighboring town, odds are you can move the reviews over. This is because the reviews are still relevant to the local area.
If you were to move from say Dallas TX to Houston TX, it might be a lot harder to have all your reviews moved to your new Google My Business listing. The reason is, the reviews are no longer based upon the local area they originally were. Businesses heavily tied to their locations might fight it much harder to move their reviews over. Examples are hotels, golf courses, or scenic attractions.
An example where reviews would be removed is if your business went through a complete brand change. For example, a new owner took over and the name changes from Joe's Shoe Repair to Sally's Flip Flops, your reviews will likely all be removed. But minor changes to the name such as Joes Shoe Repair LLC is fine.