Value in tag "name" for a river crossing several countries (i18n)

I would say that all along the river should have the international name:<lang> and in each country the respective name in name. If the river makes the border, both names are equally valid, and since no name is bad I would use both separating them with a semicolon is probably the correct syntax, but (unlike separation with a slash or a dash) it will not look good on renderings (just a remark, tag correctly).

The river-as-border is the tricky case (for border-crossing rivers, just split the river into multiple parts and tag each accordingly). But multi-value tagging is both ugly and a cop-out.

You'll have to be subjective here. Does the river border one country for longer than the other ? Is the official administrative boundary shifted towards one of the riverbanks ? Is there more boat traffic from one country than the other ? Is one of the countries more internationaly influencial ?

Just choose one version and learn to be happy with it. It will not be perfect, but such is the fate of the "name" tag. Once that's done, put the other version in an "alt_name" tag.

Different parts of the same river can have different names. If you have a top level relation with all the "name:< lang >=" tags and subrelations for each country with the name=.

The only problems are rivers that is used as a border where the locals on each side have different names for it. This is the same problem as where there are two equal languages spoken in a region. There have been a lot of debate about this. I think that puting name=< lang A >;< lang B > is the best option.

River-as-border: since not all renderers support the "name:<lang>" tags, I think it's good practice to provide a default "name" tag as a fallback value. The Rhine river, bordering France and Germany, is probably a good example.

http://www.openstreetmap.org/browse/way/91320954

To remain neutral, names in the "name" tag could simply be in Unicode alphabetical order.

If the river borders many countries, using all the names on the "name" tag would be too verbose I think. You may consider a system of relations: one "master" relation for the entire river, using only "name:<lang>" and without a "name" tag; and one "minor" relation for each part of the river that borders a pair of countries, including "name:<lang>" for the languages of these two countries and a fallback "name" tag combining these two names.

This has several advantages: the "master" relation can be linked from the main Wikipedia article; the "master" and the "minor" relations would be returned by Nominatim and would fit different user's needs; there's no need to tag each way individually, minimizing maintenance; most maps (particularly Mapnik) would render an acceptable river name.

Note: some ways in the Rhine have a "note" tag saying that the "name" tag must include both names. This may indicate that naming only the relations is not enough for proper rendering.