Yes, the locomotive was named after him. He was also Deputy Chairman of LNER.This possibility is from Wikipedia, so the accuracy is not guaranteed. There is an entry for Higham Park:
Higham Park - Wikipedia
which refers (about 2/3 of the way down, under the heading 'Highland Court') to a Walter Whigham, chairman of Robert Fleming and Company, Merchant Bank.
I am not 100% sure that the above mentioned gentleman was the Walter K. Whigham the locomotive was named after, so would welcome better-informed opinion.