Naming has a large arbitrary and cultural component and so is subject to the same structures as fashion. It seems for many centuries the only choices for Western Europe were Christian saint's names and for men mostly just the apostles.
But fashions change. It seems like in 19th c. Americans, the fashionable source was Old Testament prophets with z's and k's (Ezekiel, Zebulon, Zachariah).
And lately (early 21st c) American girls are named after president's last names (the aforementioned Madison, plus Kennedy, Reagan, Taylor (this is the answer to one of the questions). This is simply a current fashion trend mostly likely to be replaced soon from some new set.
One subtle pattern in English speaking areas for at least the past two centuries is to name a boy using the maiden name of the mother, usually a second or third boy since the first got the full name of the father (with Jr. or III appended).
As trends go, people sometimes follow the external view of the phenomenon (last names for first), which accounts for Jefferson Davis or (much later) Harrison Ford, whose mother's maiden names did not supply their first names. That these first names are the last names of famous people (American presidents) probably helped in their choice.
I think it simply follows from the natural stress patterns of the English language. See here. Two syllable nouns generally have the stress on the first syllable. Many 3 syllable nouns also do. Words that depart from the natural stress patterns tend to be words borrowed from other languages, and there is a tendency for them to eventually get coerced into the native pattern if they are in the language long enough.
There might be something of interest to explore if female names are more likely to depart from that pattern--there may be a greater tendency to want to use foreign names or foreign pronunciations with female names, having to do with cultural notions of masculinity and feminimity (e.g. good Saxon words considered to sound manly, vs fancy French words).
Best Answer
According to wikipedia, the appropriate terms are Eastern order and Western order. The wikipedia article says:
The article doesn't address what use (or not) of a middle name is called, except for brief discussion of Patronymics and Matronymics and saint's names as middle names.