Multiple Enemies Animator Problem

I am new here and hop my post is in the right forum. A couple weeks ago I started programming with C# and Unity and now I would like to build a little Mario Game for my school project. This worked very well so far. But now I have got a problem with the Goomba enemy’s. All the 10 enemies are using the same script because I do not want to write 10 scripts for 10 identical objects. But if the Player Mario jumps on the head of one enemy and kills him, the Enemy-Script set the Death Boolean Animator Preference to true for every Enemy. So all the 10 Enemies start immediately with the Death Animation. How can I force only one enemy to start the Death animation rather than all together.

Any hint is highly appreciated

Thanks in advance