It depends on the contact type. You can merge clients in the Clients screen. CORE moves all the time and expenses, projects, invoices, payments or any transactions linked with the client to the selected destination client. Check out CORE Help for details on that. Check out this video on merging data in CORE.
However, you cannot merge employees. A quick work-around for this is to move the time entries from one employee to the other, and then delete the obsolete/unwanted one.