To unlock the Making a Name For Yourself trophy in FIFA 19, you will need to earn a total of 2,000 FUT Champ Points.
You earn FUT Champ Points after completing Division Rivals matches in Ultimate Team. You will be awarded a varying number of points depending on if you win/lose/draw. The number of points earned varies depending on which division you are playing in.
The points earned won't be reset each week, so you can play at your leisure until you accrue a total of 2,000. Once you hit the 2,000 requirement, you can spend the points on a Weekend League entry and the trophy will unlock.