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Yes, it was McCullough who awarded them with Single of the Week.
When did the surname start to slip out?
That's a good question... I'm sure there must be something earlier but the New Musical Express article "Look Back in Wrangler" from 1996 explicitly exposes Lawrence's surname.
(Links to this piece in the Articles section seem to be broken so here is the text.)
Acording to this:
Lawrence used the stage name Jon Lawrence, probably for a time, then dropped "his" first name.