Honestly? It might cause issues. Japanese people are anal about these things. If I were you I'd ask for a correction of this document.
Japan Life
For people already living in Japan - anything relevant to living or working in Japan such as lifestyle, food, style, environment, education, technology, housing, work, visas, sport etc.
The best way to once and truly solve this would be to register a 通称名 (Tsūshō-mei), which is like a legal alias.
You can do this at city hall, provided you have evidence of its use.
I used my health card, and a bank card, which both had my katakana written.
Although my English name has multiple middle names, my katakana doesn’t have them. So, doing this has made my life much easier.
In my case, all official mail from the city now comes addressed to that name. Also, it is printed as an addition in the front of the my number card.
Oh nice, that's good to know. I'll try that. Still, with my pension book, the problem was that someone, somewhere just transcribed my name without me being there and now I have to try to fix that. I don't know if that registration would fix it (but maybe it does help sometimes).
Anyway, thanks!