A conversation on Twitter prompted me to do an idle check to see what US trademarks Saul Zaentz currently (as of July 2020) has active in regards to Tolkien properties - in case anyone finds this useful information. This can change over time as filings expire or are abandoned, and new ones are filed. Also it is good to note that the Saul Zaentz Company has the rights to many, many more names and terms that those covered in the list of active trademarks below. When and how they trademark certain things depends largely on what licenses they are issuing or considering, for example. Just because a character or place location is not on the list below does not mean that it is free to be used!

The home page for the US PTO search page is http://tmsearch.uspto.gov/

I poked around using various search terms, but had the best luck just searching for "Zaentz" in the Owner Name field.

Over seven hundred trademarks are currently active, when you include all the various permutations - depending on how the filing was done, contested, and modified, there could be, for example, half a dozen different trademarks issued for the same words but in different formats, like on T-shirts, boardgames, etc.

A quick and dirty, unsorted list of what I found. You will notice a few oddities - it appears that an occasional way that Zaentz resolves disputes is for Zaentz to trademark the disputed business name and then license it back to the other party (with unknown terms).

AN UNEXPECTED JOURNEY
ANDURIL
ARAGORN
ARKENSTONE
ARWEN
ARWEN EVENSTAR
BALROG
BARD THE BOWMAN
BATTLE OF FIVE ARMIES
BEORN
BILBO
BILBO BAGGINS
BOLG
CONQUER THE WORLD BENEATH
DAIN THE DWARF
DESOLATION OF SMAUG
ELROND
EOWYN
EREBOR
EVENSTAR
FARAMIR
FELLOWSHIP OF THE RING
FRODO
FRODO BAGGINS
FRODO'S PIZZA
GALADRIEL
GALADRIEL EVENDIM
GANDALF
GANDALF THE WHITE
GANDALF THE WIZARD-CLOWN
GIMLI
GLAMDRING
GOLLUM
GONDOR
GREEN DRAGON
GUARDIANS OF MIDDLE-EARTH
GWAIHIR
HOBBIT
HOBBITAT
HOBBITON
HOBBITS OF THE SHIRE
KHAZAD DUM
KILI THE DWARF
LA COMARCA
LE SEIGNEUR DES ANNEAUX
LEGEND OF FRODO
LEGOLAS
LEGOLAS GREENLEAF
LORD OF THE RINGS ONLINE
LOTHLORIEN
LOTR
M-E
M-E MIDDLE-EARTH
M-E MIDDLE-EARTH ENTERPRISES
MIDDLE EARTH
MIDDLE-EARTH QUEST
MIDDLE-EARTH: SHADOW OF MORDOR
MINAS TIRITH
MINES OF MORIA
MISTY MOUNTAINS
MITHRIL
MORDOR
MORIA
MOUNT DOOM
MY PRECIOUS
MY PRECIOUSSS
NARSIL
NENYA
ONE RING
ONE RING TO RULE THEM ALL
ORC
PALANTIR
PRANCING PONY
RADAGAST
RIDERS OF ROHAN
RINGWRAITH
RIVENDELL
RIVENDELL BICYCLE WORKS
ROHAN
ROHAN NUTRITION
RULE THEM ALL
SAMWISE GAMGEE
SARUMAN
SAURON
SAVE THE SHIRE
SHADOWS OF ANGMAR
SHELOB
SHIRE
SIEGE OF MIRKWOOD
SMAUG
SMAUG THE DRAGON
STING
STRIDER
TAURIEL
THE BATTLE FOR MIDDLE-EARTH
THE BATTLE OF THE FIVE ARMIES
THE FELLOWSHIP
THE FELLOWSHIP OF THE RING
THE HOBBIT
THE HOBBIT AN UNEXPECTED JOURNEY
THE HOBBIT THE BATTLE OF THE FIVE ARMIES
THE HOBBIT: AN UNEXPECTED JOURNEY
THE LORD OF THE RINGS
THE LORD OF THE RINGS THE FELLOWSHIP OF THE RING
THE LORD OF THE RINGS THE RETURN OF THE KING
THE LORD OF THE RINGS THE TWO TOWERS
THE LORD OF THE RINGS: ARAGORN'S QUEST
THE LORD OF THE RINGS: CONQUEST
THE LORD OF THE RINGS: MIDDLE-EARTH DEFENSE
THE LORD OF THE RINGS: WAR IN THE NORTH
THE LOTRO BEACON
THE ONE RING
THE RETURN OF THE KING
THE RISE OF THE WITCH-KING
THE SCENT OF MITHRIL
THE SHIRE
THE SHIRE'S REST
THE TWO TOWERS
THE WHITE COUNCIL
THERE AND BACK AGAIN
THORIN OAKENSHIELD
TREEBEARD
URUK-HAI
WAR OF THE RING
WAR OF THE RINGS
WITCH KING
YAZNEG

An interesting article about a Poultry company named ROHAN that was contested