Jackson Whistle is moving to the Giants from the Kelowna Rockets who play in the Western Hockey League in Canada.
The 21-year-old's father is Dave Whistle who led the Giants to league and play-off titles during his period in charge from 2000 to 2003.
First choice goaltender Murphy, from Dundee, has signed on for an eighth season with the Giants.
The 34-year-old has won the British Netminder of the Year award eight times.
Steve Thornton, Head of Operations at the Giants, said: "The decision to sign Stephen Murphy is one of the easiest for me to make each year.
"He has been the backbone of our organisation since I signed him back in 2009."
The Belfast Giants have signed the son of their first ever coach as back-up netminder to number one Stephen Murphy.