Is there a name for synonyms that appear to have opposite meanings?

How about false enemies?

I originally voted to close because I thought synonym was an adequate generic term here, but Stephen's comment re false friends prompted me to Google language "false enemies". It seems clear that this coinage has occurred to others (here it is in a Wikipedia talk page, for example).

The first other "clear-cut" example I came up with was ravel / unravel, but I've found a couple more since, as have others here - maybe OP's right, we need a word to Know thine enemy!

EDIT: If an out-and-out neologism is acceptable, there's always the crypto- prefix (secret, hidden, or concealed), so they could be cryptosynonyms (though I must admit that one doesn't yet seem to have occurred to anyone else within the scope of Google's indexing routines).

According to Wikipedia:

"Flammable and inflammable both mean capable of burning. The word "inflammable" came from Latin inflammāre = "to set fire to," where the prefix "in-" means "in" as in "indoctrinate", rather than "not" as in "invisible" and "ineligible". Nonetheless, "inflammable" is often erroneously thought to mean "non-flammable"."

http://en.wikipedia.org/wiki/Flammability#Linguistics:_flammable_vs._inflammable

I don't think there's a name for this -- it's just that the latin prefix "in" can mean either "not" (as "indiscreet") or also literally "in", as in "in-flames"-able.

No, there is no word for describing such pairs. It is because the etymology of both the "in" prefixes are different. The in- in inflammable was derived from the Latin preposition meaning en- (like en-flamed) and not the Latin prefix meaning -un.

There is a related concept neologistically known as the "contranym" or "antagonym", which is words which mean two opposite things, so for example "to Cleave" can mean "to sever", or "to adhere tightly".

Obviously the concept you're looking for is the precise opposite of this. Can I therefore suggest that by analogy these words ought to be called "homogenyms" (from "homogeneous" meaning "essentially alike")?

(I initially wanted to suggest "homonyms", but that's already taken.)