Murray now hopes to win a first Test cap as Wales begin against Fiji on Sunday, 10 November at Principality Stadium, before playing Australia (17 November) and South Africa (23 November) in Cardiff.
Whether his parents will fly over for those games remains to be seen.
“I’m not sure, they really want to,” said Murray.
“Unfortunately they’ve already booked flights for a couple of weeks later for when we play Glasgow on 29 November.
“They were planning on watching one of my Scarlets games but whether or not they can come a bit earlier or not we’ll see, but hopefully.”
Murray was able to celebrate with his Scarlets team-mate and house-mate Taine Plumtree with the back rower also named in the squad.
“He’s stoked as well,” said Murray.
“You have to be when you get the opportunity to play international rugby. We went out for dinner as a little celebratory dinner and we’re both chuffed.”
One thing Murray will have to do if he gets his chance is become familiar with the words of the Welsh national anthem.
“I haven’t learned that yet, but I’m sure I’ll be practicing in the shower or something!” said Murray.
“I’ll definitely have to get on to that.”