About this name "Asuka Kagura"
Can I find any source that even has that name? From the sources I know, I have never heard that name. Because all the major sources would've had that name if it was ever used in the show.
Only RangerWiki uses this name no one has heard of, and other sources are just direct translations
"What's his name?"
A while back there was some dispute going on regarding Shurikenger's real name, and I'm here with good evidence to prove that his real name is unknown. But first a little bit of backstory:
Since the 2000s every Kamen Rider and Super Sentai season will have an ultimate compilation guidebook published some time after their run on TV has ended, released under the Chouzenshuu (超全集) banner. The most recent one released was that of Kamen Rider Ex-Aid, which included comprehensive information on every single character, form, monster, device, episode and movie from Ex-Aid. You could say this is one major definitive source we're missing out on, since they're all in Japanese, and not many of us would bother buying these guidebooks if we don't understand them.
Luckily, a Facebook user going by the handle of A.So.Ku413 has been generous enough to take snapshots of these guidebooks and uploading them onto Facebook. Here's a link to his page: https://www.facebook.com/pg/A.So.Ku413/posts/?ref=page_internal (scroll down to find all the posts)
Here is a compilation of what he has grabbed from the Hurricaneger guidebook: https://www.facebook.com/A.So.Ku413/posts/1623423611116650
Of note is the bio page for Shurikenger: https://scontent-sin6-1.xx.fbcdn.net/v/t1.0-9/19555014_1623423211116690_6830022208843774868_n.jpg?oh=be5439d9d8e585f115cfe0800f225a00&oe=5B4A3566
While the other rangers have their full name and everything else about them written out and illustrated, Shurikenger's bio doesn't reveal his full name, and continues to keep his true identity a secret (bear in mind that this guidebook was released after the season's end).
This, coupled with the fact that searching up his supposed full name in Japanese gives results about a completely different character (I won't elaborate more), should be decisive enough to prove that Shurikenger has no known real name at all.