English/Scottish Naming Patterns

Not cast in stone, but commonly used...

Males
First-born Son - father's father
Second-born Son - mother's father (OR father's grandfather, in which case everything shifts down a notch;
i.e. 3rd son is named for mother's father and 4th for father, etc.)
Third-born Son - father
Fourth-born Son - father's eldest brother
Fifth-born Son - father's 2nd oldest brother or mother's oldest brother

Females
First-born Daughter - mother's mother
Second-born Daughter - father's mother
Third-born Daughter - mother (or father's grandmother, followed by mother's grandmother)
Fourth-born Daughter - mother's eldest sister
Fifth-born Daughter - mother's 2nd oldest sister or father's oldest sister

2nd wife's oldest daughter named after the first wife, using her full name

A comment from somebody: Most families only follow the naming patterns
for the first 2-3 children. The
English are more likely to use the names of their own brothers and
sisters first.  Then they will use their own names and finally their
parents' names, if the family is large enough.  The English also seemed
to have more of a tendency to use "celebrity" names...kings, governors,
local doctors, etc.

An extract of an article by Kathleen Much:
Practices varied by region in both the colonies and England. Probably the most
common pattern was 1st son for paternal grandfather, 2nd son for
maternal grandfather, 3rd son for father or uncle, successive sons for
other male relatives or very occasionally godfathers or friends. This
pattern holds well into the 18th c, after which we see more biblical
names in protestant families and honorifics (naming a child after a
famous unrelated person, particularly political or military) in less
devout ones.

One assumption that is statistically valid is that if you find a set
of brothers who each name a son X, the father of all the brothers is
likely to be named X. If you find an alternating set of father=X,
son=Y, grandson=X over several generations, the odds are good that it
will continue backward and forward (but you can't count on this; the
pattern had to start sometime, and maybe you have the beginning of
it). Keep in mind that you may not know which son was the firstborn;
child mortality was high, and somebody named in a will as "eldest son"
may in fact have been the third or fourth boy born to a family.
Sometimes names of dead children were reused, but often they were not.

(@1996 Kathleen Much
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