The word “renege” comes from Latin, springing from the same root as the word “negate.” It is used to describe when someone goes back on a deal, especially in a legal context. For example, if someone were to promise to provide a service or some sort of product, then refused to produce it or deliver it, then they could be said to have reneged on their promise.
Properly pronounced, “renege” rhymes with “hedge,” or “wedge.” The apparent similarity of part of the word to other common racial slurs is pure coincidence.
There is nothing racist whatsoever about the word “renege.” It is not related to any racial euphemisms, it has never been used as a racial euphemism, and it has no connection whatsoever to the racial politics of modern American life. It is best known as a legal term and more closely related to terms such as “renegotiate.” Unfortunately, in this modern world, it is not difficult for people to misspell words in an attempt to be humorous. Although racist jokes related to this word have not caught on, possibly because they are not particularly funny or clever, that has never stopped crude people before.
It is an unfortunate fact of life that most racial slurs, and indeed, most slurs in general, are simple declarative words with long etymological histories. It is simply impossible to construct the English language in such a way that a word cannot be turned into a slur. Intelligent and educated individuals understand completely that no insult is intended when words are used properly.