Mammele: R’ Schachter quotes a Tshuvah by R’ Moshe, I believe (he definitely quotes someone on this), who says that those Chiyuvim were only before Mattan Torah, when those were the only things that identified us. Nowadays, we have a Torah to keep our identity. A Torah which did not give an obligation to give “Jewish” names, have distinctive clothing (though there are rules about what can be worn), or speak a certain language.
nisht and Joseph: Your argument is unfair and it doesn’t hold up. Why do I care if people incorrectly use being “Modern Orthodox” as an excuse. If I commit murder and say I did it because I’m a penguin, does that make me a penguin? Does that make all penguins murderers? It’s unfortunate that some people have confused the term “MO” with meaning “not actually Orthodox”. But that doesn’t make it true. I’m not a penguin, no matter how much I (or anyone else) claims I am.