Relation tags do not cascade down to their member elements. If you create three ways, don't ways and youdon't name them, but instead put them in a relation which does have a name tag, virtually nothing (renderer, router, analysis tool, whatever) will understand what you mean.
As the `relation:street` page says: "Note that this relation is not established and unsupported by some applications." Translation: it's been made up by someone to whose sense of data consistency it appeals, but no-one else uses it.
Relations are used for a few distinct purposes, such as route relations (buses, bike routes, etc.), multipolygons, and so on. For everything else, there is nothing wrong with having two adjacent objects which have the same tags.