I've run a few of these naming contests in my time but have nothing whatever to do with this contest, so please allow me to offer a few suggestions:
The two most popular types of name suggestions I see in asteroid naming contests are people who want to name it for themselves, or people who want to name it for friends/family members/pets, alive or deceased. There are lots of asteroids named for people's friends or family or pets, but that kind of suggestion is unlikely to win an international contest; you need to suggest a name that will have significance to more people than just you.
Another popular name theme is to suggest a name that implies that the asteroid is a threat to Earth (e.g. "Doom" or "Smashocalypse"). I am very glad to tell you that Hayabusa2's target asteroid, 1999 JU3, offers no threat to Earth, so such names don't really fit.
One last thing I've noticed is that whenever I write about a naming contest, people offer name suggestions in the comments on that post. I will not be forwarding any name suggestions from the comments section to JAXA; if you want to submit a name, please go to the application form so that JAXA will see it!