In his appendix where he discusses how he renders personal and place names in the Rohirric tongue, Tolkien admits that he was inconsistent in the way he adapted those names to English. Some names, like Shadowfax, are clearly transposed into Modern English, albeit using an archaic root "fax", meaning "mane", which is no longer current in the language; the actual Old English form would be "Sceadufæx". Other names, like Edoras, are not transposed into Modern English, but are left in their Old English form, which supposedly corresponds directly to the Rohirric language. The distinction is relevant when reading the story aloud, since Modern English and Old English have rather different pronunciation systems, e.g. the first vowel in Shadowfax is somewhat different from the first vowel in Sceadufæx, but given the spelling I assume I am meant to use the modern pronunciation.
There are some names, however, where I am not certain if I should be pronouncing them as if they were Modern or Old English, in particular Thrihyrne, Hornburg and Mundburg. For Thrihyrne, it looks fairly archaic so I am tempted to give an OE pronunciation, e.g. rendering the "y" as a high front rounded vowel and pronouncing the final "e" as a separate, short vowel. But I note that Tolkien does not use a diaeresis over the final "e", which he usually does if he intends us to pronounce it, e.g. in Gúthwinë, and not leave it silent as is usual when pronouncing Modern English spelling. So is Thrihyrne perhaps meant to be pronounced as a Modern English name, maybe something like "thri-HERN" [θrɪˈhɝn], as opposed to [ˈθriːˌhyrnɛ] or something like that?
For the names ending in "-burg", I initially assumed these should be pronounced as Old English, with a final fricative [x], since the Modern English form of the same root is "-borough" e.g. Tuckborough. But then he started using "burg" as a word on its own, to refer to the tower of the Hornburg, which surprised me, since I didn't know that "burg" was a word in Modern English, except in American English where it means "town" and is clearly derived from the many American towns that end in the German element -burg, e.g. Gettysburg. This element is etymologically related to the OE word, but has clearly come to mean something different from what Tolkien means by "burg". What do people make of this and how it should determine how we pronounce those names?