SELECT DISTINCT teacher FROM schedule WHERE teacher REGEXP '^[А-ЯЁ][а-яё]+\s[А-ЯЁ]\.[А-ЯЁ]\.$'
To use a literal instance of a special character in a regular expression, precede it by two backslash (\) characters. The MySQL parser interprets one of the backslashes, and the regular expression library interprets the other.
'^[А-ЯЁ][а-яё]+\\s[А-ЯЁ]\\.[А-ЯЁ]\\.$'