if there's an object belonging to an object belonging to an object, do you let go of most 的? For example: "Our teacher's name?" You basically say "The name of the teacher of ours" like: 他们的老师的名字. Or do you let go of one of 的? Because whenever I try to google translate anything similar, it lets go of all the 的 except for the last one. Thank you in advance.
Usually, we do not use so many "的" in a single sentence, we will just break it apart. There are always many ways of saying one thing, using many "的" in a single sentence is not a habit in Chinese.
For your example, we could let go of the first "的" or not
Sometimes you let go of the last "的"
For more "的", if it is not confusing, you could say
But in Chinese, what we would usually say is