How to get logged in username of Jenkins in parameter's Groovy script?
From the Java API documentation for hudson.model.User:


  String  getDisplayName()
  Returns the user name.
  
  String  getFullName()
  Gets the human readable name of this user.
  
  String  getId()


It's not clear to me from your question what data you want (I think it's the user ID?), so I'm not sure which of these methods will get you that data (getId()?).  But in any case, you would call the method like:

User.current().getId()