This kind of long dash is sometimes called 2倍ダッシュ, 倍角ダッシュ or ダブルダッシュ when there is a technical reason to distinguish. But untrained Japanese people call this simply as ダッシュ.
Some punctuation marks imported from Western countries tend to be wider in Japanese typography, because ordinary characters like kanji are already wider than English letters. As you said, the em-dash in Latin fonts is obviously too short in Japanese sentences.
Unfortunately, there is no simple way to reproduce this 2倍ダッシュ in HTML. One ugly but easy way is to use 全角ダッシュ (full-width dash) twice. The 全角ダッシュ should be available whenever Japanese fonts are available. The Japanese 全角ダッシュ and the English em-dash are mapped to the same character (U+2014
EM DASH) in Unicode:
The first example above uses two 全角ダッシュ directly, and the second example uses two
In my browser (Chrome on Windows), there is no visible difference between the two lines, but there is a small space between the two dashes.
If you are using a good software, this space will not be visible (at least in Japanese fonts). Some DTP applications can also automatically prevent a line break between the two dashes, effectively allowing you to treat two 全角ダッシュ as one character.