When I was doing my writeup on names of Japan I realised that I had seen somewhere that Germany had many names (in other languages). After a bit of research, here is a list derived from postings in sci.lang and faqs:

Germanus, is the latin name, and the one from which the enlgish derives. It may mean "brotherly".

Deutsch comes from a Proto-Germanic word meaning "of the people". Originally was used to distinguish the language from others. the word "Dutch" is derived from this word, and originally meant any northern germanic people. "Pennsylvania Dutch" is now used for this meaning (Pennsylvania = brotherly love?).

Many other languages derive words for Germany from the older version of Deutsch, e.g. Irish tuath, Italian tedesco. yerricde also adds that in Italian, Germania is used as a name for the country, and tedesco for the language.

Teutonic derives from the Teutons, a tribe of Germanic people in Jutland, and may be another derivative of "Deutsch".

French Allemagne and other variants come from another tribe, called the Alemanni (all the men).

Finnish people call them saksa after the saxons.

Slavic people call them nemets, meaning "dumb".