"Hello! My last name is Li."
(not sure if this'd be helpful to anyone but thought to post it anyways)
As a Chinese speaker (not quite fluent), I find it strange to introduce yourself w just your surname. I've never heard anyone do that when meeting someone for the first time. You'd introduce yourself with your surname followed by your name. (A chinese name typically consistents of the surname + 1 to 3 characters, most often 2 and least often 3)
For example(I used a celebrity's Chinese name for this), someone with the surname「李」(Li/Lee) and name 「永钦」(Yongqin) and would introduce themself like this: 「你好。我叫李永钦。」or 「你好。我是李永钦。」(subtle difference; "Hello. My name is Li Yongqin" vs. "Hello. I am Li Yongqin". Either works fine.)
If you're intoducing yourself to someone in chinese and don't have a chinese name I think you'd still introduce yourself w your surname first(I'm not sure, I recommend fact checking me).
If you want to give yourself a chinese name: For your surname I recommend picking a syllable in your last name and finding the closest phonetically similar chinese surname character. For just a regular name I'd recommend looking up name character meanings, picking 1-2, then if you can, find a native speaker to double check so that you don't accidentally give yourself a name that sounds funny/have a homonym that doesn't mean smth good.
Hopefully this'll be helpful to at least one person. ¯_(ツ)_/¯