"To give someone space" I was looking for the equal word of "to give someone space" in Chinese and found this :


  给我一点空间。


I'm not sure if 空间 is the correct word though. 空间 means "space" but I think it refers to a visible one.

While the "space" that I mean here is like giving someone some me-time, giving them time to be just alone, or letting them do whatever they like without us being too clingy.

Now, can I still use 空间 to refer to that kind of space?
Sure, the expression you had is correct and indeed used in daily life. There are however, some alternatives which you could use

请给我一点自由空间
请给他一些自由
给我一些自己的时间