"Von Hessen und bei Rhein" is correct but the confusion is understandable. In general speak the historic principality is still best known as Hessen-Darmstadt.
For three centuries it was the Landgraftschaft Hessen-Darmstadt (principality of the Landgrave of Hessen-Darmstadt). In 1806 it became the Grand Duchy of Hessen but already in 1871 it became "just" a memberstate in the Reich.
Even under the Grand-Duchy itself there was confusion with the old name, with references to the "Grand Duke of Hessen-Darmstadt" while indeed the princes and princesses were known as "Von Hessen und bei Rhein".
The glorious era of independent and strong Hessen-Darmstadt was (and is still) overshadowing the somewhat non-descript short intermezzo of the Von Hessen und bei Rhein era.