Maybe.
Ronald (6 Letters) Wilson (6 Letters) Reagan (6 Letters)
FWIW—Wilson was his Mother’s maiden name, and he was born about a year and a half before Woodrow was nominated.
Hieronymus, I don’t think you’ve cited info that would suggest anything other than chance in there being six letters in each of RWR’s given names.
There’s no generally-known evidence his dad Jack was ever member of a secret society by the time Ron was born. If Jack had been on the police force or more well-to-do, we might think differently.
His mother’s affiliation with the Disciples of Christ suggests she would have been attuned to and would likely have quickly turned away from anyone associated with a secret society, as many among the Disciples know of the ultimate involvement of non-Christian entities being worshiped among, for example, Masons.
For what it’s worth, I spent several years in Dixon, IL, where Reagan grew up. I knew people there from among the Disciples of Christ church and had an office in 1980 in the same building Reagan used for his Hometown/County Presidential Campaign Headquarters.
By contrast, there is evidence Barry’s birth date was contrived and that those involved in his life were heavily into secret societies.