FTP, what name is shared by this theorem and the vector appearing in it, which is derived not from what the vector does but from the name of its discoverer?
This theorem can be derived by applying Ampere's Law to the work-energy theorem and then using Faraday's law to eliminate the curl of E.  The power delivered by a set of electromagnetic fields is equal to the time derivative of the sum of electric and magnetic energy densities, plus a new term involving the flux integral of a namesake vector.  Equal to E cross B divided by the permeability, this vector gives the energy flux density of a propagating field.  FTP, what name is shared by this theorem and the vector appearing in it, which is derived not from what the vector does but from the name of its discoverer?
This theorem can be derived by applying Ampere's Law to the work-energy theorem and then using Faraday's law to eliminate the curl of E.  
Poynting's theorem or Poynting vector