I assume that your are using the Invoices starter solution? (There are many, many invoicing databases out there.)
If so, enter layout mode, select the Invoice Print Layout and edit the layout to add your company name and logo.
"Also, if I add people to the contact management: will they show up in the "customers" section in Invoices?"
Data entered into the contact management starter solution will not automatically appear in the Invoices starter solution. These are completely separate invoices.