Referencing Springer products: what name to use for the publisher? For references to Springer products, I have come across a lot of names for the publisher, (and all of those are present in my own Mendeley library):


Springer Science+Business Media
Springer-Verlag
Springer


Is there a difference, or can I just go and standardize my library to one of them (preferably Springer. In my area, mathematics, there is no chance of confusion with Springer Publishing, and even less with Axel Springer SE)? 

Also, is there a difference between the locations [New York|Heidelberg|Berlin|a combination of the previous] usually found along with Springer, or can I just standardize my library to always use Berlin, since that's where the headquarters are? I understand Springer has major offices in the other cities, but do different books really pertain to those different offices, and does this need to be made clear in the References?

If the answers to one of the questions is no, do you have a hint where to find the correct information? The first pages of the books that I have sometimes list all of the above options in different places. Furthermore, for example my copy of V.I. Arnold's "Mathematical Methods of Classical Mechanics, Second Edition" says "© 2010 Springer Science+Business Media, Inc." without any mentioning of "Springer-Verlag", whereas the website says "Publisher: Springer-Verlag New York".
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.