Well @XeroChess in this petition proposal you did not specify how much you would be willing to pay for such feature, for starters. Secondly there is plenty of way to store your games. Like SCID database in some cloud service. There is also scid for android. So this is very non interesting proposal

You can set the study on private and you can also add names and ratings

The study is already a list and you can put the names of the players on it.

If you PGN the games correctly; the players names, ratings, date of the game, tournament name, board number, will all show up in a game imported into a study.

For my tounrament games I currently use which is good, but would be even better (using a non-profit good for the world)
@petri999 you said "how much would you be willing to pay?" lichess is a 501c3 non profit, they would never charge people for a feauture like that. I would be willing to donate money to them for a feature like this.

As you can see in this study it is already possible to add names to the sides of the board:
You can either add them in the PGN or go to the "tags" tab on the bottom of the study and define the "white" and "black" tabs to be the names of the players, and the names will appear on the top and bottom of the board.

Intresting, I think that this is good but lichess needs to clearly create a tab FULLY designed for mainly entering in personal tournament chess games. It still is a study tab and is not as refined as a true database like SCID or chessbase.