If you are distilling a true finished beer that has been brewed and/or fermented with hops you will not be allowed to call it whiskey in the USA. It will have to be approved as a Distilled Spirits Specialty and you will be required to put a statement on the bottle that says something along the lines of "spirits Distilled from Barley and Hops". Of course there are examples of products made this way that call themselves whiskey, but they were either approved by the TTB in error or the producer is just not being truthful in their formula and COLA. For it to be called Malt Whiskey Flavored with Hops or Hop Flavored Malt Whiskey it would have to meet the TTB definition for Whiskey first (mashed from grain only, distilled under 160p, aged in new charred oak at under 125p) before the hops are added. Adding hops into the mash, ferment, still, or barrel (unless after it has already been aged for the desired period) will push it into DSS and require the appropriate class and type statement.
I know this because I have been through this multiple times. It is frustrating but at least the TTB has started consistently applying the rules.