If you have the requirement to store SharePoint documents using a specific account, you must make sure this account has access to the Azure Portal and the specific Azure subscription. In this example, I had a logic app UploadToSharePoint. Each logic app has a property API Connections. If you edit the API Connection for SharePoint, you will get the screen below.
In this case I want to use a specific account DevESB@a-hak.nl. This account is entered in field Display Name. Next, we have to click [Authorize]. Now, what happens is, that your SharePoint connection is validated using the account with which you are logged in to the Azure Portal, in this case firstname.lastname@example.org. That’s the problem. First you have to log in to Azure using account DevESB@a-hak.nl. Then you can go to the API Connection and click [Authorize]. Now it works.