According to the McCune-Reischauer (MR) system, the Korean alphabet was spelled out as

The diacritic marks (breves and apostrophes) were dropped because they were cumbersome to write. In July 2000, Korea introduced the revised Romanization system. It changed hangul to hangeul.
After seven years, the new system is maturing amid criticism. Some institutions in Seoul are, however, still insisting on using the spelling hangul rather than hangeul and ``fighting'' the revised system.
Look, however, what the Anglophones have done to the word


Webster Online and the Merriam-Webster (MW) Online Open Dictionary list both hangul and hangeul as English words. So does Wicktionary. It states that hangeul is preferred to hangul. MW Online lists hangul but not hangeul. It lists, however, Busan and Incheon.
These are the revised spellings, like hangeul, of Pusan and Inchon, respectively. MW Online is catching up with the new Romanization of Korean words. Neither hangeul nor hangul is listed, however, in Cambridge Dictionaries Online, Ask.Oxford, and YourDictionary.com.
Thus, both hangeul and hangul are not ``full-fledged'' English words because they are not listed in all dictionaries. Google hits on hangul vs. hangeul run about 2.7 to 1, which used to be about 10 to 1 in 2004. Thus, the word hangeul is gaining ground. In French and German Wikipedias, hanguel, not hangul, is an article title word.
The new Romanization system is still drawing criticism. No Romanization or written language system is perfect. Look at English. ``Why the sound sh can be written as ce (as in ocean), ti (as in nation), or ss (as in issue)?'' ― by Jared Diamond, Discovery (June 1, 1994). The Taipei Times anguished over Chinese Romanization (June 25, 2000): ``This obfuscation of Chinese even extends to the subway system, where a silky feminine voice coos `Tam-shooey' instead of the proper `dan-shui'. Mispronouncing station names in a caricatured foreigner accent only makes it harder for visitors to get familiar with Taipei, since this is not what we hear on the street."
To Koreans, Romanized Korean words according to the MR system did not sound like Korean (e.g., Pusan for Busan). Other countries all have their share of problems with Romanization. Even two of the three leading Japanese Romanization systems write si and pronounce it as shi as does the new system, one of the reasons of criticisms by linguists.
Anglophones expect Romanization systems to serve their needs first. They complain about the revised system because it ``Koreanized'' the MR system. They should recognize, however, that the new system helps non-Koreans speak Korean words more like Koreans than did the MR system.
King Sejong first introduced hangeul in the book he titled Hunmin Jeongeum or ``The Correct Sounds for Teaching People.'' The spelling hangul has corrupted the correct sound.
The spelling hangeul can, however, restore and maintain the correct Korean sound. The word hangul must fade away before it does more damage (i.e., corrupt, anglicize, or Americanize the correct sound).
It makes little sense to insist on using hangul, not hangeul, simply because Anglophones like hangul better or hangul has already ``crystallized'' more as an English word than hangeul.
Not all English dictionaries list hangul as an English word. Insisting on hangul (and the MR system) will only promote confusion about Korean word Romanization among Koreans and non-Koreans alike.
Use hangeul. Otherwise, hangul may corrupt itself further to hanggool or hangkool. Anglophones may soon force Koreans to use hanggool as an English word for the Korean alphabet.
This can be averted by not using hangul now. Use hangeul and conform to the new system. The sooner the word hangul is put away along with the MR system, the better Korea will be.
Yun Chung is a retired Korean engineer, residing in the San Francisco Bay Area since 1955. He is trying to improve the image of Korea in the Anglosphere by reporting errors in Korean government English websites. The writer can be reached at yunchung2@msn.com.