Thanks, but it's the wrong family

I'm looking for Arthur Hall & Herbert Lake who lived there in 1902 (according to the London, England, School Admissions and Discharges, 1840-1911 records on ancestry).
It's been a family mystery for ages as my granddad always said that his dad (Herbert Lake), used to have the surname Hall. Now I seem to have found evidence, but it seems a bit odd that his father (Arthur Hall), didn't change his name too? Very strange.....
I think I'm going to spend the rest of my evening searching......
