Hi there, Esther17520.
When importing transactions on your register, there is a file format that QuickBooks Online (QBO) accepts. You can either use 3-column or 4-column.
As of now importing the details including the account customer description is not an option. In the meantime, what you can do is to add a note on the Memo field when reviewing and categorizing your data.
To know more about importing your transactions, see below articles:
If you need more help, let me know by commenting below. I'm always around to help. Have a nice day.