Did the companion book through a travel agent or directly through the cruiseline? In either case teh payment is charged directly by the cruiseline. If the booking was done directly through the Cruise line then you should be able to call them and give them your credit card for your half. If a TA was used then the agent will have to call in the payment to the cruiseline. Most cruiselines will have travel agent locators on their websites. You can use this tool to verify the agency that the companion is using. You can also verify the agency by looking them up independantly and calling to speak with them. Credit card (NOT a debit card with visa or MC logo) is best. This way you can dispute and unauthorized charges before you pay them If you pay with check or a debit card you have to fight to get back money you already paid. Your credit card company will offer the best protection. If the other passenger has already paid the balance and wants you to pay them, then it gets tricky. Many cruiselines will allow a TA to refund part of the payment back to the original card and then immediatly charge the other portion to a different card. This way you would be using your card for your half and still have your protections. Paypal is a waste of time and offers little or no protections. This person is not shipping you anything. If they do not have a merchant paypal account you can not use a credit card and must pay from your bank account. Kiss that goodbye if there is a problem.
Again the best way to do it is to each pay your own half on a credit card through a REAL Travel agent and not some big online cruise discount website. Pick a specific agent with a direct phone number from a verifiable office. You'll get the best service this way as well and you will not pay anymore than if you book elsewhere. Most cruiselines prohibit any agency from selling a cruise cheaper than their lowest website price.