Do Japanese ever assign a name to a typhoon, or are they always numbered? In most countries the name is more commonly used.
Yes, they are named according to the conventions, but colloquially they are more or less always referred to by their ordinal number (reset every year).
The only place I personally can remember having seen the names mentioned in Japanese is on the website of Japan's Meteorological Agency (JMA). See e.g. this one:
The JMA has the official responsibility of naming Typhoons in the vicinity of Japan, where they cycle through a list of names. However there is also the PAGASA (Philippines) "unofficially" naming some of them. For details, please see the extensive Wiki article: https://en.wikipedia.org/wiki/Tropical_cyclone_naming#Western_Pacific_Ocean_(180%C2%B0_%E2%80%93_100%C2%B0E)