The reason it says "change with caution" is because your business name becomes your URL or basically your "address", so you may direct some potential clients there now and then you change it later, this creates confusion...as the link is no longer valid.
Please only change this if you really need to.
If you have changed your business name on your/profile, then it has changed your URL.
The only way to "correct" this, would be to change your business name back to what it was before or alternatively to redirect the old URL to the new one.
It is only an issue if you have already shared the URL link with potential/clients, those people will no longer be able to find your page by clicking on the "old" URL link. They will still be able to find you via the usual searches (eg Google search, etc).
If you have included the URL link on any advertising (eg business cards etc), it would also need to be changed.
If you absolutely do need to change your business name (URL) and would like to redirect the old URL (business name) to a new URL, please email firstname.lastname@example.org for assistance.