Hi Ian
I thought that this would be easy but it's not. Presumably you have seen some index entry which just gives his name age and town. Looking for William Davidson on Ancestry I can see three faintly possible (indexed as Son but born about 1897 or 1899) and also one indexed as Grandson, born about 1897. They are all born in Gateshead and living in Gateshead on the night of the census. Three of them have indications of a second forename, the only solo William is in the following household:
RG 13/4752 28 p47 38 Hewitt Street
Jonn Davidson Head Married 34 Organ Builder (Worker) b. Northumberland, Newcastle
Isabella do Wife Married 35 b. Durham, Gateshead
Emley do Daur 10 b. do do
John do Son 5 b. do do
Isabella do Daur 4 b. do do
William do Son 2 b. do do
James do Son 6 months b. do do
All the best
Gobbo