No. It will only create or update the customer in QuickBooks when you create an invoice for them. Once the invoice syncs, it will add the customer to QB if they do not exist, or update them if they do.
If you do not want to create an invoice, you will need to add or edit the customer manually in QB.
This also applies to QuickBooks Online.
Does it have to match the name exactly to not add a new customer or is there a method to match the syncro name to the quickbooks name?
Syncro will try to match before creating a new customer. It will try to match by the email address, phone number, or name. If only the name is available in QB, it would have to be exact. This is why we also use the email and phone number as identifiers.