Origin of street names ending in "-hurst"
Solution 1:
One reference: hurst = wooded hill. In street names, it's likely to be a modern invention; in place names, it may well survive from antiquity.
It's a Saxon word, and would thus probably occur more in Southern England than the Danelaw in the north. OED has
Etymology: Old English hyrst < Old Germanic type *hursti-z, whence Old High German, Middle High German hurst, German dialect horst ‘heap, cluster, thicket, top of rock, sandbank’ (Flügel); Middle Low German horst hill, wooded or bushy eminence, small wood, Low German horst, host, a bushy piece of land surrounded with marsh, a wooded eminence, East Frisian hörst, horst, höst, thicket, copse, sandy eminence (probably formerly overgrown with brushwood); Middle Dutch horst (Kilian horscht, horst) thicket of brushwood. In the forms -hurst, -hirst, -herst, a frequent element in place-names, as in Hawkhurst, Chislehurst, Ferniehirst, Amherst. (So -horst in Dutch and Low German.)
Icelandic hrjóstr rough place, barren rocky place, Norwegian dialect rust, ryst, little wood, thicket, clump of alders and dwarf birch, wooded tract on a mountain, lateral ridge of a mountain, Faroese rust ridge, show similarity of sense, but are difficult to connect phonologically.
Solution 2:
Hurst appears to mean a wooded hill according to this site. It is an old part of a name but only local research could tell you whether a road was ancient or had just been given a name made up from old roots to imbue a sense of history and rootedness.
Solution 3:
Hurst (and also hirst and sometimes corrupted over time to est) comes from the Old English hyrst which could mean a copse, a hill or both; a hill with a copse on it.
In English names then, it suggests an origin prior to the Battle of Hastings and the coming of the Normans, though the existence of such names in America and Australia should be enough to demonstrate that it's possible for somewhere with that name to have been founded after 1066, and just named in imitation of the form used elsewhere.