Yes, like Sophia said, it's an abbreviation for William. Social Security didn't exist prior to 1935, so any data from 1880-1934 all came from applications typically submitted by the bearer of the name (rather than their parents as is done today)-- so if, say, a William Benjamin Jones submitted an application and he wrote his name down as Wm Benj Jones, Wm is what would go into the data, even though it's not his "real name".
Here is a list of other abbreviations. A few others made the charts as well, but are less noticeable because they look more like nicknames/real names (Chas for Charles, Geo for George, Robt for Robert):
https://en.wiktionary.org/wiki/Appendix:Abbreviations_for_English_given_names
Isadora Evander Larkin
Pax Symphorian Grey
www.behindthename.com/pnl/59411