online chess kind of snail /mail chess in the olden days. Its like 1 move per day or maximum 14 days (that depends on how you or your opponent set it). So i kind of don't understand your question.
BTW, even at otb chess, you are not allowed to write notes except the moves. So can you explain further what you are exactly looking for.
If you want to write notes, you must write them about the position, not about your move.
It is the position that suggests the moves. Take notes about the position, and evaluating your notes, you might consider some candidate moves and then try them with the analyze board.
However I dont' play online chess this way, I have got too many games in progress and besides in an OTB game you cannot either move the pieces before to see the future positions, either take notes!
I try to play online chess to improve, but I can't think of a move and write notes at the same time because I get distracted. How should I do?