It's just interesting that we are finding other riders called "Thomas", but back home, it certainly appears that he was just known as "Wally". On Tuesday, December 27, 1932, Monica Park Speedway in Christchurch hosted an Interprovincial contest between Canterbury and Wellington, with Wally Kilmister and Charlie Blacklock as captains. Also on the bill was a "Chevrolet Gold Helmet Race between Wally Thomas and Norm Gray.
The following month, Wally faced Percy Lunn in a challenge race, while there was a three-cornered match race between Kilmister, Blacklock, and Eric Whittle.
There was an article on Speedwayplus which featured all New Zealanders who raced in the UK, and Wally's name isn't listed.