Is a salesperson's payment of money from his own pocket to a client to complete a sales transaction considered a bribe, and is this act permissible or forbidden?

If the client is purchasing for himself, or for a company with its knowledge and permission, then there is no harm in paying him the commission, and it is not considered a bribe. However, if he takes the money for himself without his company's knowledge, or if his taking of the money affects the company's interest—such as buying unnecessary items or at a higher price—then this is considered a forbidden bribe that is impermissible to pay.