That doesn't apply here; no matter how much street name data is collected, no amount of the collection, including the entire thing, can be copyrighted in a way that would impose any restrictions on OpenStreetMap.

From your link, which is quite short:

> such copyright may exist when the materials in the compilation (or "collective work") are selected, coordinated, or arranged creatively such that a new work is produced. Copyright does not exist when content is compiled without creativity, such as in the production of a telephone directory.

So you'd have to ask yourself, "was any creativity, of any kind at all, required in order to call this street by its own name?" And the answer is even more obviously "no" than in the paradigm case in which the telephone directory can't be copyrighted because it consists of facts (involving no creativity) in an externally specified order (alphabetical) in a collection specified by an external rule ("everything is included").

On that page:

  facts are not copyrightable

..compilations are, but you're obtaining a copyright on the compilation, not the facts.

No they aren't, but there is such a thing as a database right which is separate from copyright. This is why OSM changed from a Creative Commons licence (a copyright licence) to ODbL (a database licence).

> but there is such a thing as a database right which is separate from copyright

That's purely an unforced error on the part of OpenStreetMap. They are incorporated in England, which recognizes a database right. But there is no reason for that. In general, there is no such thing as a database right.

And this isn't even relevant to londons_explore's point; he is stupidly arguing that even if the information is available on a road sign, the public cannot use it because it might be included in a protected work somewhere. That is obviously untrue; the availability on the road sign does in fact automatically mean that inclusion in a protected work is irrelevant.

If you see a sign giving you the name of a road, and then publish information to the effect that the road's name is what is printed on that sign, no database was involved at any point, and a database right cannot apply. All you have is a bare fact.