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nominee

They will typically just use a corporate nominee i.e ABC Company Ltd will be named as director or shareholder. Some do use real people however sometimes.
 
Depends.

Professional outfits where they are regulated by someone with some teeth are going to retain and use real people.

Trust and company service providers in the UK, for example, are (ahem, should be) overseen for MLR compliance by HMRC. The problem for one of them of whom I'm aware was the inability to recruit UK resident nominees and balance the number of bank accounts they could open for UK LTDs before the banks blackballed them.

I've dealt with agents in Seychelles and Belize, both geared to selling to professional resellers, and in one instance, I was able to verify the local resident director and shareholder in one of those jurisdictions was very real as a friend of a friend outside the sector was actually a relative of the nominee.