I'd say most well educated people would know what an anagram is. I'd adapt my language according to who I'm talking to.

There are some really smart people here on ITALKI. I know that an anagram is some type of word play, but even I have to look it up to see what it is exactly. It is used infrequently, unless you hang around a group of people who love word puzzles.

There are two parts to your question. Yes, most people know what an anagram is. It's the same as synonym or eponymous. People know what it means, because it comes up if you study written words long enough. That said most people do not use the word in daily conversation, but that is only because it rarely comes up. Just because something is a low frequency word, does not mean that it is not well known. So yes, understood by many, but used very infrequently. Go right ahead and use it.

My guess is that almost every native English speaker knows what an anagram is. . They tend to be puzzles and so are used in education & by people who just enjoy puzzles & intellectual pursuits. . "Anagram" is just another word. Best to learn it & the meaning, then it will cause you no more trouble. :)

Thank you for every one. My teacher live in Japan long time. Many be he forgot some words or he would give a chance to thinking about this word:D