Could be a few things. It's still part of Westconnex (and the signs going onto it say that) but it's different in that the M8 is and won't be not the only part of it. Some people could probably still call it the "New M5" too, which... y'know.
As it stands, the M8 is just signed as "Tunnel" (as is standard for tunnels with numbers) which bothers me a bit.
Lane Cove Tunnel is an oddity in that it has both name and number signed - modern day NSW standards would probably sign it "Tunnel" too.
Cross City Tunnel and NorthConnex also get passes on that given they have no number.