Warning: source:name without name

Why do I get warning: source:name without name?
Even if the tag has a value?

Whereabouts are you editing when you get that warning? Can you give an example of the exact location - you can zoom right in at osm.org and paste the URL here.

Also, are you getting this warning in an OSM editor, or somewhere else?

Because [source:name] should be used with [name].

Thanks for answers!

The problem was as maro21 said, the area had no name tag.
I also got a warning of missing ‘ref’ for ‘source:ref’.

If I add a name and ref tag, the warnings disappears.

But should these tags be used any longer?
In this case should I add the missing tags, or delete all source* tags?

Quite likely these ways were either tagged en masse or copied from a way which did have a name and/or ref, with the relevant source:* tag being missed. I would say it is OK to remove the tags, but in general I would only do so if actually editing them: fixing very minor inconsistencies will bump up the version number and sometimes can give the impression that someone has actually updated mapping in the area rather than just looking at some QA tools.