Combobox with a lot of (thousands) of options

in my project there is a form. One of the field is problematic for me. User should choose an option from a very long list (thousands of options). I wanted to do it by combobox, but I don't know how searching should works.

We can't display options after typing by user first letter, because list will be still very long .

I thought that we could display options after 3 letters.

Example:

User have to choose one name from the list (10 000 of names).

Is it clear? Do you have any ideas do it better?

The most important is that user must choose an option from the list (can't type new name) and list is veeeery long.