Hey Gregory,
Can you please post a screenshot of an example customer who only has their Name added to the Bill-to address? I can try replicating the process and verify if it syncs over or I receive a conflict.
From what I understand the integration between your webstore and QB: it creates a new customer and inputs the 'FirstName LastName' into the first line of Bill-to address.
<BillAddress>
<Addr1>John Smith</Addr1>
</BillAddress>
Is that correct?
-- Mortaza