I found a couple of entries in the New York Times "After Deadline" column useful.
In precise, traditional usage, an “eponym” is someone or something
that gives its name to something else. So “eponymous” describes the
giver of the name, NOT the receiver. A restaurateur named Joe Smith
could be described as the eponymous owner of Joe Smith’s Restaurant,
but the establishment is not “Mr. Smith’s eponymous restaurant.”
(The opposite problem often occurs with “namesake.” That word properly
describes the receiver of the name — a grandchild may be the namesake
of her grandmother, but not the other way around.)
So the only ones of your examples that have the correct use of “eponymous” are those that describe the giver (the bridge) and not the receiver. And conversely, only in #6 is “namesake” used correctly.
The second entry is more pertinent to the use of “eponymous:”
Sometimes I quibble over words we overuse. Sometimes I complain about
words that are misused. And sometimes I take issue with words that
seem pretentious or contrived.
Then there’s “eponymous,” which could fit any of those categories.
In precise use, an eponym is someone who gives a name to something
else, and “eponymous” describes the source of the name, not the
More often than not, we and others muddle this distinction. And often,
there’s a way to say what we mean without using “eponymous” at all. So
let’s use it sparingly, and wisely.
Edit: For reference, the entry for eponym from Wordsmith.org, one of my favorite resources:
eponym (EP-uh-nim) noun
A person, real or imaginary, from whom something, as a tribe, nation, or place, takes or is said to take its name.
A word based on or derived from a person's name.
Any ancient official whose name was used to designate his year of office.