Currently in NAF and LCSH, "Mogul" is the preferred form for Mogul/Mughal Empire. I noticed in the 2403 Tentative List a revision proposal for Gardens, Mogul Empire being changed to Gardens, Mughal Empire.
The proposal has a note that says:
952 | | | | | $a To align with Mughal Empire NAR change |
The revised NAR isn't at authorities.loc.gov yet but I guess it's coming. Strangely, there aren't bunches of proposed revisions to other LCSH records like Art, Mogul Empire, Architecture, Mogul Empire, and Painting, Mogul Empire. Wait for list 2404, I guess.
Sherman