As a minimum, you should always capture the following details about a new individual customer:
Their FULL name
Current Address
Mobile Number
Email Address
Your invoices are supposed to have at least the first two in most situations, so you need to capture that anyway.
If you are giving any sort of credit, get their date of birth and identification, e.g. a copy of their driver’s license.
If they won’t provide this, you don’t want to risk them as a customer.