Don't know entirely if this question is allowed but in doing some searching two leading contenders seems to be the Winged Hussars of the Polish-Lithuanian commonwealth or the Ostrogoths.
Ostrogoths appear to match the names Theoden, Theodred, Eomer but other than that I knew very little of the Ostrogoths culture.
Tolkien's Kingdom of Rohan is somewhat based on the Goths, but is also heavily influenced by Anglo-Saxon England and, to some extent, early medieval Scandinavia. Tolkien was a lecturer in early medieval languages and based the language of the Rohirrim - later dubbed 'Rohirric' mostly in Old English. Most Rohirric names are Old English names, especially those which adopt the "-đing" suffix but some of his placenames - Westfold for example - are Scandinavian.
There was some cultural influence from the Goths; like the Goths, the Rohirrim were a largely horse-based society who moved into the geo-political orbit of the eastern successor state of a former great Empire [Gondor is Byzantium by any other name] but the society of Rohan itself is largely drawn from Anglo-Saxon and Scandinavian sources, even down to their relationship with the Dunlendings, who are allegories for the Brythonic population superceded by the Anglo-Saxons.
If you want some further reading I recently finished reading a great source study anthology on Tolkien by Jason Fisher called, well, Tolkien and the Study of his sources: Critical Essays. Two in particular seem relevant to this discussion, “Byzantium, New Rome!” Goths, Langobards, and Byzantium in The Lord of the Rings by Miryam Librán-Moreno and The Rohirrim: “Anglo-Saxons on Horseback”? An Inquiry into Tolkien’s Use of Sources by Thomas Honegger.