Why have we named this proto language proto-Germanic?
Apparently it developed in southern Scandinavia. Then expanded (via migration or contact?) towards what's now Germany.
I wonder why linguists chose to name it "proto-Germanic", instead of any other name. Why are all these languages considered "Germanic" instead of e.g. Scandinavian?
Roman authors, at the latest from the time of Caesar, used "Germani" to identify all the "Germanic" tribes on both sides of the Rhine. So this usage has been established for a long time.
It's also worth pointing out the term originates in German as Urgermanisch or Protogermanisch, and that the German for German is Deutsch, not Germanisch. It was intended to be more neutral w.r.t. living Germanic (germanische) languages than it ended up sounding in English.
The other answers have all touched on different aspects of the question, but I'll try to combine them.
Thousands of years ago, the Romans named much of north-central Europe Germānia, and the people who lived there Germānī (and things from that area Germānicus). It's unclear where this word came from; it's probably not related to the native Latin word germānus "of siblings", but no proposal for its origin seems to have really caught on.
Germānicus was borrowed into modern German as germanische, "Germanic", referring to the old Roman territory and the tribes who lived there. It's notably not the German word for "German", as in "from Germany"—that's deutsch. And as far as I know, it's not really associated with any modern state or ethnic group. It's just a technical term, used when talking about the Roman-era province or the language family including English, German, and others. (It's unclear how many of the Germānī spoke Germanic languages, for that matter, but that's less important—they share a name because they're both associated with that particular region of Europe.)
Why not call it "Scandinavian"? Because Roman-era Germānia was a larger region, and a lot of early research into Germanic languages happened within Germānia but not in Scandinavia, and in languages other than English, it generally isn't the name of a modern region—and when the name was being chosen, nobody knew where the language family originated.
Names are to a good part conventions. It is historically long established to name the group of languages consisting of the Scandinavian languages (Norwegian, Swedish, Danish, Icelandic; but not Finnish or Sami), German and Dutch, Frisian and English, Gothic and some more related languages "Germanic". The protolanguage is named Proto-Germanic because of the the linguistic grouping, the naming does not make any assumption where Proto-Germanic was spoken.
According to Cornelio Tácito tells us in his De origine et situ Germanorum ("Of the origin and territory of the Germans"), the gentilicio Germans comes from the eponymous of a god: "They celebrate the ancient songs, which is the only kind of memories and annals they have, to a god named Tuiston, born of the earth, and his son Manno, who is said to be from whom these people originated ... "(Celebrant carminibus antiquis, quod unum apud illos memoriae et annalium genus est, Tuistonem deum terra editum. Ei filium Mannum, originem gentis conditoremque,…, Tac. Germ., 2). Manno had three children, and the descendants of one of them they were called "Herminones". But the name Germania was relatively recent [for his time] (Ceterum Germaniae vocabulum recens et). But what Tacitus here clearly refers to is the Gentile for all Germans, since clearly, as he goes on relating, the Germans were a tribe that she was the first to cross the river Rhine and drive out the Gauls; that tribe were the Tungros, who were then called Germans (ac nunc Tungri, tunc Germani vocati synt) [* some editions change from Germanos to Tungros, but for this purpose it does not matter to us]. In this way, Tacitus leads us to the origin of name, and also explains its popularization and extension towards the nomination of other adjacent tribes. "So the name of this nation, not the name of the people, was gradually gaining strength, and all the others at first took the name of the victorious, due to the fear that it imposed, so that they invented themselves and called themselves by the name of Germanos "(ita nationis nomen, non gentis evaluisse paulatim, ut omnes primum a victore ob metum, mox etiam a se ipsis, invention nomine Germani vocarentur. Tac. Germ., 2). What is lost in later interpretations is the name of the god, from which Deutsch derives, which gives rise to the name of the nation Deutschland (land of the Teutons). The variations in writing are due to an oral tradition from which the phonetic meaning was being collected. But look where you look at the gentilicio -germano- derives from the eponymous of the god. That god is the same civilizing god that the Egyptians called Thoth. Plato calls it Θευθ (Pl. Phdr., 274c; Phlb., 18b) and on the Rosetta Stone he appears as Θουθ (Rosetta Stone, 1, 49). In Latin Cicero calls him Theuth (ND., 3, 22, 56) and Lactantius Thoyth (Instit. Div., 1, 6, 3). And as Cicero confirms us in the same passage that god is the Argifonte (killer of Argos) and the one who after killing Argos fled to Egypt where he invented writing and bequeathed laws to the Egyptians, and in Egypt they called him Theuth [Mercury] (hunc Aegyptii Theuth appellant). Mercury is the name Latin that was given to Hermes (Greek god). Hermes is a civilizing god and philanthropist. According to the Homeric Hymn to Hermes, he was the argiphon and the god interpreter (hence 'hermeneutics'). Thus Theuth (Teut, Deutsch), as well as Tuiston, whence come the Tungros or Teutons, is the same Hermes and his descendants -Hermogenes- Herminones, where Germanos comes from. So that the Germans are the descendants of Hermes or Teut, who according to Tacitus, It was only the name of a tribe, but as they were brave warriors, for having expelled the Gauls from the other side of the Rhine, the other tribes were adopting the same name.
