Scotland's People for some reason don't show mother's maiden names which would have helped in looking for any siblings for William.
The reason why SP does not show mothers' maiden surnames is that this information was not included in the original indexes. What SP has is the indexes as they were compiled by the GROS. Mothers' maiden names were not included in the births index until 1929. This is less than the 100-year cut-off for viewing birth certificates online, and GROS has decided that mothers' maiden surnames will not be shown on SP's online index of births less than 100 years ago.
They are gradually adding mothers' maiden surnames to the older birth indexes (from 1855) but there is a long way to go until they get to 1916, let alone 1928.
Mothers' names, including their maiden surnames, are indeed shown on Scottish marriage certificates, and the names of the parents of the deceased should be shown on all death certificates, assuming of course that the informant knew this information.
BTW All Scottish BMD indexes, unlike the England and Wales ones from 1911 onwards, always show middle names in full unless someone has so many middle names that the full name is too long to fit in the index.