Origin of Benjamin as an evolved form of ancient place name elements:-
Food for thought.
Ancient word evolutions and deformations due to local usage in England are well recorded unlike fanciful suppositions of names based on Biblical Personal Names.
Cornish : ben "foot, base, stump" Cornish : pen "head" Welsh : bôn "base, root, stump" Irish: bun "base, stump" also "river-mouth, estuary"
Most ancient place names containing "ben" were later changed through local usage to "pen". In the most ancient names, "p" is interchangeable with "b" as they are not distinguished in many ancient dialects and languages.
Most place names with the true origin "ben" lie at the foot of rivers or streams unlike those true names in "pen" which lie at the head. There is a similar usage with Scottish Gaelic "bun" and Irish "bun".
Note also: Breton "Ben-" meaning " mouth of a river".
Note particularly the example of "Banastère" from Old Breton"Bonester" (now obsolete) and Middle Breton "Benester" (now obsolete).
Poignant for the most ancient of Benjamin families is the Cornish "benyges" meaning "blessed"; the ppp of the verb "benyga" "bless"; Welsh "bendigo; and Breton "binniga~n".
An "i" was at periods in ancient times and in some languages e.g. Nordic interchangeable with "j" and "y".
The "a" was a word common to many old languages to denote the possessive or adjectival. The "-i" is a name suffix in Cornish in river names mostly. "yn" means "narrow" in Cornish; And, "-a" meaning "place of" is of obscure origins, but "a" as preposition means "of". Cornish "gahen" meaning "henbane" ("Hen" (like Hel) a Nordic tribe:region) giving Ben+gahen
Benyges + men giving "The blessed men" - perhaps druid ? or "The baptized men" - from times before Christianity and/or evolving to the start of Christianity.
There is a lot of work needed in the study of place name origins.
In genealogical research place names of surrounding regions of founding or earliest known families could contain exceptional indications of ancient origins. Take care to record them along with family records if among the fortunate who have the opportunity to travel to original sites. Try to include any local indications of earliest known names of places even verbal records in old dialects. The best records and most ancient can remain in local archives or collections or even archaeological remains only available on location. National archives and registries were subject to very old manipulations notably in the 16th and 17th centuries. They can be far from a definitive authority of family origins.