To unlock the Remember the Name trophy in FIFA 19, you will need to play the Division Rivals mode of Ultimate Team.
You will be award points for each game of Division Rivals that you play based on your performance that will count towards your weekly rank. You will receive point regardless of if you win, lose or draw (not to be confused with Skill points).
There are five different ranking levels, and the number of points required will change throughout. The points required resets every Thursday. As soon as you hit Rank 3, the trophy will unlock. You won't have to be Rank 3 at the end of the week.
If you go for this on a Thursday after the weekly reset, you should be able to achieve rank 3 within 2 games if you win.