Referencing Springer products: what name to use for the publisher?
The suffix "-Verlag" basically just means "publisher" or "publishing company in German. Therefore, I would include it only if other companies in English—such as Dover Publications, for instance—also appear with the "publishing" term in their listings. If they don't, I'd eliminate the "-Verlag" for consistency.

As for the others, those tend to be "imprints" within the publishing house. In general, I believe these can also be omitted, particularly in "abbreviated" citation styles. In longer styles where full details are provided, you may provide this information; if the publisher doesn't want to include it, they can remove it when editing the proofs.