First example. "Lina is a student", "Li is a student". Please notice that "Li" is a substring of "Lina".
Second example. "Vladimir is a student", "Vladislav is a student", here they partially match, namely first 5 letters (Vladi) are exactly the same.
What should I change in my notation in order to deal with such cases? Of course I have enough fantasy to make up my own notation to deal with it, but I wonder if there is "official" way (or ways).
There isn't any official way to do it. If you want to use $\dagger$ for Li and $わ$ for Lina, you're welcome to do that.
The only real requirement is that you're consistent, and that you do not use those symbols for anything else. As a second thing, which is nice to aim for but not a requirement at all, is that it is easy for your readers to remember which is which.