It's syntactically valid to omit the preposition of in OP's examples, but idiomatically uncommon. A bit of background from britannica.com on Toponymy (taxonomic study of place-names)...
Habitation and feature names are either generic or specific, or a combination of the two. A generic name refers to a class of names such as river, mountain, or town. A specific name serves to restrict or modify the meaning of the place-name.
We only usually only use the "combined" naming convention if it's contextually important to specify the "generic" component - either because the "specific" element is likely to be unfamiliar to the audience, or to disambiguate (State of New York, City of New York).
I would say the default is that if specified, the generic component is normally followed by of [SpecificName] with "population centre" place names (village, town, city). But "geographical features" are often referred to using the specific component as an initial-position adjective (Table Mountain, the River Thames). Note that the river of [RiverName] is extremely unlikely, but the Forest of [ForestName] and [ForestName] Forest are both in common use.
Unfortunately, the situation is complicated by things like Mount Everest, where the optional generic mount = mountain has effectively been incorporated into a "double-barrelled proper noun" (and nobody ever refers to the mountain [of] Everest or Everest mountain), and County Kildare (rarely the county [of] Kildare). It's also worth noting the capitalisation of proper nouns such as The Forest of Dean is in the county of Gloucestershire.
In short, there are no clear-cut rules as to which format would be used for any given referent. But as a general principle, the preposition of should be included in any reference where the "specific" component is unfamiliar or ambiguous, unless you're already aware that for the specific case in point, a different convention has become firmly established.