Purchases for a sole proprietor as a private person or as a company

Can you simply make purchases for your sole proprietorship in your own name and then enter them as expenses in your sole proprietorship? To do this, I often ordered from websites (or in stores) in my own name so that I could pay the vAT immediately and then enter it as a business expense. I work with vAT exemption, so I don’t necessarily need an invoice for every purchase in order to recover the vAT.

This didn’t seem to be a problem for the Peppol obligation, but now that everything from suppliers and business customers has to go through Peppol, I wonder if this is still possible. After all, some websites don’t allow you to make purchases in the name of your company. It’s also convenient for me to pay the vAT at the time of purchase.