First, stop writing "wanna." Just don't do it ever again. Second, I would probably say "See-yong" and you would say "No, it's pronounced 'Sung'" and then I would repeat "Sung." And we would go on with the conversation. In the US (and I'm sure in the UK and Australia and NZ and other majority English speaking countries), lots of people have names that you can't guess the pronunciation from the spelling. If you do come as a student, the first day of every class, the teacher will read through the names, and get about half of them wrong - not just people from other countries, but people whose parents and grandparents were born and raised in the US. Don't worry about it. Write it however you want. You do want to make sure you're consistent every single place you've written your name. I have friends from countries that did not use the roman alphabet and weren't careful about the spelling of their names. They had problems all the time trying to convince some official or other that they were both "Seong" and "Sung."

This is a very personal choice. But I think if I were to read "Seong" I would trip over it a tiny bit and then pronounce it like "Song" in my mind. Not a major problem though. I think "Sung" would flow a tiny bit easier if I read it because it has an easy English pronunciation. Neither name has any bad connotations. Go with whichever feels best to you!

We don't use the "eo" vowel combination in English. If your name sounds like sung, you should spell it "Sung". If people do say "soong" , it is just because of their accent, and there is not much you can do about that. ( A Scottish person might say "soong" because that is how they say that vowel, but most people will say "sung") . But "Seong " is impossible to know how to pronounce, so people will say "song" or "see-ong" or something else, they will NOT say "sung".

If I had never seen "seong" before, I would guess that it sounded like "see-ahng". I think I have heard other Americans pronouncing it that way. If Americans aren't familiar with any Asian language, they will pronounce "Sung" with the vowel in "butter". If they are familiar with Chinese names but not Korean names, they will pronounce it like "soong". They will also probably guess that you are Chinese instead of Korean. There are a couple of other romanization schemes. The McCune–Reischauer system would write 성 as "song" The Yale system would write it as "seng". I feel like if you showed "seng" to a group of average Americans, half would pronounce it more-or-less like 성, and half would pronounce it like "sang". In short, no spelling will produce the right pronunciation all the time. Mispronouncing foreign names is a hallmark of American culture. When you come here, we WILL mispronounce your name, no matter which spelling you choose. :(