[Mithadan]

Gothmog was the name of the chief of the Balrogs in the First Age. I think Tolkien's use of this name was intentional and signifies that the Third Age Gothmog is not a mere Orc chieftain but rather an entity of significant power. When I first read LoTR, or at least before I made any connection between the names, I assumed that Gothmog (TA) was a Nazgul. I also note that the actual quote from LoTR is "Gothmog the lieutenant of Morgul" which also strongly suggests a Nazgul. Making Gothmog second in command for the Battle of the Pelennor is not necessarily inconsistent with Khamul being "second to the Chief [Nazgul]". Khamul may simply have had other duties in the battle. Also, as Khamul was resident in charge of Dol Guldur, the legions of Morgul may have been better inclined to follow a leader they were familiar with, the lieutenant of that city.

While Khamul may have been the second "highest ranking" of the Nazgul at least per Unfinished Tales, we must keep also in mind that The Hunt for the Ring is truly unfinished. Christopher Tolkien comments that portions of the draft were superseded by The Tale of Years and JRRT had not prepared this excerpt for publication. While I hate to raise the issue of canon, I wonder if Tolkien would have modified his description of Khamul if he compared this draft with LoTR or perhaps clarified his "ranking" with regards to Gothmog.

As an aside, Tolkien was notorious for not reusing names (there are some exceptions such as Glorfindel, who was apparently the same Elf in the First and Third Ages notwithstanding his death). Yet he had no problem reusing the name Grond so perhaps it is not surprising that he chose to reuse Gothmog.