In QuickBooks Online (QBO), the ability to add new customer that has the same name with the existing ones is currently unavailable. This also applies to vendors and employees.
As a workaround, you can add extra character to the new customer's name so the system will not treat this as a duplicate.
I'll pass along your suggestion to our Product Developers. They're always looking for ideas to consider on how to improve QBO. In the meantime, I recommend visiting our Blog site. This is where we share recent happenings and future developments, such as updates to newly added features.