How do you refer to a hyponym that is the same word as the hypernym?
According to "The Dictionary of Linguistics and Phonetics", these are autohyponyms. The example they use says:
...for example, a cow contrasts with a horse at one level, but at a lower level it contrasts with bull (in effect, 'a cow is a kind of cow').
Similarly, the term peacock is often used to refer to the entire family of birds, rather than calling them peafowl (and hence peahen and peachick).
I myself like a cup of coffee. No, not a mocha or a latte, just a plain coffee please.
In "Pride and Prejudice", Jane Bennet is often referred to as Miss Bennet, being the eldest of the girls. She is of course one of the Miss Bennets, but when this is used in the singular, it refers to her specifically rather than to any of her sisters.
There is a brand of fashion store called Somewhere, with many outlets which are somewhere.
While Levi's are best known for their Levi's, they also sell t-shirts and jackets in addition to their jeans.
As a final example, I offer you the word word, which is also an autonym. All autonyms are subsets of one in the set which they describe.
A famous example of hypernymy intersecting with polysemy involves the word animal. If one accepts dictionary definitions as being authoritative rather than insisting on a purely scientific register, using the first two definitions (in reverse order) given in 'Collins English Dictionary – Complete and Unabridged 2003', we can restate a mammal is a type of animal as an animal is a type of animal. Of course, such crazy mixing of registers is inadvisable though not strictly wrong. We avoid such absurdities as:
Fifty years ago, gas was a mixture of gases.
Salt is one example of a salt, and sugar is one example of a sugar.
Cast iron is mainly iron.
To answer your second question, I think many brand names suffer from this problem especially when commoditization occurs. For example, "No that's a tissue paper; I would like a Kleenex specifically." Is not something you're going to hear a lot, but it's still possible.
Other examples include: Asprin, Jello, Band-Aid...
Example that is not a brand name: china (could mean tableware or tableware made in china specifically). I'm using the dictionary here; I've never personally used the second definition.
Related question with cool map
PC is another example: "personal computer" includes Macintosh computers (Macs) and IBM-compatible computers (PCs).
Are there any other examples of a hypernym being the same as the hyponym, creating a disambiguation problem?
The word man is a good example, where man can refer to either the entire human population, or else to roughly half of it, sometimes leading to charges of language insensitivity, when the original language may not have been intended to infer exclusion.
"Man shall not live by bread alone" doesn't exclude women, obviously. But that's not always so easy to determine when the plural is used; for example: "Now is the time for all good men to come to the aid of their country."