If you have a client who you sometimes engage as a vendor for some of your work, you may have created a vendor profile with the same name in CORE. However, when you try to sync the vendor record from CORE to Xero Accounting after already having synced the client, you will get an error. This is because when you send clients and vendors to Xero, they go to the All Contacts list there. They are mapped as customers and suppliers only after you start syncing their invoices and vendor bills. Check CORE Help Center for details on that.
So, if a client and vendor have the same Display As name, they cannot be sent as unique IDs to the All Contacts list. The simplest way to resolve this is to change the Display As of the vendor to something different so that you can sync it as a unique ID to the All Contacts list.