What is this part called?

Probably the upper strut (shocks are in the rear) bearing/insulator.

https://www.rockauto.com/en/catalog/cadillac,2000,eldorado,4.6l+v8,1361416,suspension

Jack up the front and extend the struts - shoot a stream of ArmorAll or Son Of A Gun up in there. See if it helps.

Cadillac Forums is full of Cadillac info for your Eldorado Eldorado Sport Coupe.......

Looks like a dust cap on the piston rod - strut has to come out to replace it. Drive the car.

Kicker is, those (ETC ???) VIN 9 CVRSS active electrical struts are made of Unobtainium and are scary hideously expensive IF you find them.

If that's strut oil leaking under that dust cap it's only a matter of time before you convert all 4 corners to Monroe passive struts and shocks. Basscatt is the resident guru on Monroe conversions.

ETC or ESC ??? Please update your profile - 2 VERY different cars, parts and service-wise.