I’ve always referred to their entire network as TWiT. If memory serves me correctly, all their shows (not just This Week in Tech) used to begin with a bumper that said “Netcasts you love, from people you trust. This.....is TWiT.”
They actually do, yes. Source: Listened to many Leo Laporte podcasts over the years, but stopped a couple of years ago, due to the noise/ads to content ratio.
I used to listen to TWiT but signed up for Audible based on their recommendation of the service and I stopped listening to podcasts and listen to audiobooks!
TWiT is the network as a whole. This Week in Tech is just one show (the original show?) on the TWiT network along with Windows Weekly, Security Now, etc.