Yes, if the user who is logged in and printing a document has at least one of the following options set — First Name, Last Name, or Title — in the Tools > Users in Company menu, this information will be printed on documents such as invoices, orders, etc.
However, not all documents include this information — customization of the relevant print reports would be required.
If you are interested in having these customizations made, please contact our customer support and specify which reports you need the information added to.