I think most people have explained it pretty well already–middle names are generally used in the US, but they certainly aren’t necessary, and are used for the reasons stated above (or before). Middle names are generally more on the superfluous side, I guess you could say? Like an extra bonus. Like one of the previous posters said, people generally don’t know someone else’s middle name unless they’re close, so no, if I were to meet an [name_m]Edward[/name_m] [name_m]Johnson[/name_m], I wouldn’t assume that he didn’t have a MN, just that it wasn’t shared. In general, most Americans don’t share their middle names unless it was a special occasion–as in a graduation, school application, or wedding ceremony, as the pp said, as well. It can be a subject of great interest in school children (I remember conversations that went like, “Oh, what’s your middle name? Oh, what’s yours?” etc.), but professionally, they’re generally not used all that much, and I’m not sure they have a ton of use, besides disambiguation (for example, [name_f]Anna[/name_f] [name_f]Madeleine[/name_f] [name_m]Smith[/name_m] is the only real easy way of telling that she’s different from [name_f]Anna[/name_f] [name_f]Zinnia[/name_f] [name_m]Smith[/name_m]), and I’ve heard it also helps with security, making it less easy for your identity to be stolen. I think the assumption, rather, is that everyone has a middle name, but they just don’t share it. I think people generally just introduce themselves as what they want to be called by. I think when someone is introducing someone else, especially in a professional setting, they’ll use the full first and last name, as in, “Oh, [name_m]Henry[/name_m], do you know [name_f]Amelia[/name_f] [name_m]Ferrars[/name_m]?” And then [name_f]Amelia[/name_f] can feel free to say, “Oh, please call me [name_f]Mia[/name_f]” or whatever. In a lot of scenarios, though, when someone introduces someone else, they’ll use whatever they’re familiar with (like introducing a friend to another friend, or a parent introducing a child), like, “[name_f]Nora[/name_f], I’d like you to meet my friend, [name_f]Addy[/name_f],” even if her full name is [name_f]Adelaide[/name_f] or [name_u]Addison[/name_u]. I think it’s just simpler that way. I knew a guy named Siont@y [name_m]Russell[/name_m] [name_m]Antonius[/name_m] [name_m]Ramon[/name_m] [name_m]Lewi[/name_m]$, which was his full name, and if we went around calling full names like that, it would be confusing and rather long and drawn out pretty quickly! So middle names are used, just not very often in everyday life, and I think it’s a lovely idea to use a Chinese middle name to honor family or your heritage. If she wants to be known by her Chinese name, she can, or she can be known as her American name.
Good luck!