And how does the person at the other end of the line react? When I answer "hallo" in Germany, the response I usually get is silence followed by "who are you?" with a surprise tone in the voice

, is it the same for you?
Because of this kind of reaction, I reached the conclusion that it is considered rude to answer "hallo" in Germany.
In
Austria customs are similar to Germany, usually you answer with your name. (It was and partly even still is normal to answer the phone, if you are visiting a friend, with the friend's family name only or with "bei" + family name - meaning: this is family/household XXX speaking, rather than mentioning your own name - of course, this is only valid if you are good enough friends to consider answering the phone of your friend.)
But this already is changing rapidly due to the fact that on mobile phones usually you
do know who is calling, and even else phones with displays showing the caller (if of course the caller is registered in your virtual phone book) are spreading rapidly.
For once, on
mobile phones the most common answer to an unknown caller has long since changed to
"Hallo" here in Austria, at least in the northern and eastern region where I live - and on cable phones the "Hallo" isn't the exception any more.
So I don't think anyone would be upset here in Austria if you don't say your name when answering the phone but "Hallo" or something similar.
However, for
business conversation (doesn't matter wether on mobile or cable phone) there still apply the "traditional" rules that you should be answering with
both company name and surname plus an additional greeting phrase, in this order, and it is considered obligatory to say good bye at the end of the conversation - at least unless you know the person you are talking to very good and have secretly agreed on it being okay hanging up on each other without (which is extremely rare but exists).
And if you know the caller then of course there are a great many possibilities to answer the phone.
With one of my business contacts (situated in Vienna, as I am) who I know very good already I usually answer with "Grüss Sie, Frau XXX" or even with "Frau XXX, was gibt's" which would be considered extremely rude if you hadn't established this 'code' of sorts beforehand.
(And yes, this Frau too could say to me "Herr XXX, ich hätt schon wieder ..." without me feeling offended in the least.

)