if my client's checking account name is only one word and quickbooks payment link account holder field is rejecting it. How can they get around this ?

I understand how important it is to ensure the payment process works seamlessly for your business, Bill.
 

QuickBooks requires a valid first and last name when processing payments. Since your client's business name only has one word, I recommend exploring a 3rd party application to meet your needs.
 

Feel free to reach out if you need further assistance regarding processing payments.

@NicoleAscencionS  RE: QuickBooks requires a valid first and last name when processing payments.

The OP didn't ask about anyone's first and last name.  They asked about the business's name.