Going up my paternal line:
My GG Grandfather was Thomas Arnold Brown
My G Grandfather was Frederic Thomas Brown, his middle name being his father's first name.
My Grandfather was Hugh Arnold Brown, therefore given his grandfather's middle name.
My father was Roger Wyeth Bateman Brown. his two middle names were the maiden names of his grandmothers.
My name is Philip Michael Brown, both names being those chosen by my parents as fashionable at the time of my birth and names they liked.
So in summary, naming convention has probably changed over the years or diverted away from any convention or pattern of old.