"What counts as a small company vtuber?"

Any japanese vtuber that isn't part of Hololive or Nijisanji

"How do I find Japanese Vtubers?"

Search for "Vtuber" plus a japanese search term and sort by "live". Here's some examples!
耐久 (Endurance)
歌枠 (Utawaku, aka Karaoke)
お絵描き (Drawing)
雑談 (Zatsudan)
料理​ (Cooking)
英語のお勉強 (Studying English)
マイクラ (Minecraft)

You can also try the following terms
新人Vtuber (New Vtuber)
個人Vtuber (Independent Vtuber)
JPVtuber (Make sure youtube doesn't correct you to JP Vtuber or you'll get a lot of polluted results)

If you want a general list of up-and-coming newbies(albeit with ENtubers mixed in), you can use this site
https://virtual-youtuber.userlocal.jp/document/ranking/beginner?order=fav_cnt_diff

"There are companies aside from Nijisanji and Hololive?"

Yes there are! Here's a list of some of the notable ones!
774 - The biggest little company, ranked 3rd after Hololive and Nijisanji. Consists of Animare(animal girls), HoneyStrap/SugarLyric(demonic shop girls), and VApArt(...apartment girls). Has a dedicated thread on /jp/
.Live - If you've heard about Sio and ever wondered about her backstory before the 5ch posts, this is the company she pretty much destroyed. She quit whilst making a lot of heavy accusations about management, and at the time everyone believed her. They never really recovered.
Re:Act - Formerly known as Kagayaki Stars. Was a black company that literally graduated a girl midstream. Supposedly better now(Hopefully for Yukino's sake)
"Brave Group" - Formerly Unlimited, A company so black it should be operated out of africa. Literally fired chuubas and replaced their VAs.
Axel-V - Company that made a big splash with their initial advertisement push but has kind of petered out. Their girl Kokuri uses Lingodeer instead of Duolingo
Virtual eSports Project - Started back during the PUBG boom as girls playing PUBG, gradually shifted to girls playing apex, now just girls doing whatever(but still a lot of apex)
Vivid - Bigger on bilibili than youtube. Notable for having a member that speaks completely fluent english, but despite this the company doesn't give a shit about pandering to EOPs.
ProproProduction - Proof that it's possible to cuck an entire country, got big off taiwanese fans and then sent their biggest talent to bilibili.
Noripro - Agency where all the members share the same artist(Norio), divided into the Idol Group and the Variety Group with the differences being those in the Idol Group doesn't interact with men and doesn't use crude jokes.
Zero Project - I don't know anything about them but their girl Rei advertises her streams as welcoming EOPs, so she pops up in a lot of people's recommendations. Apparently has an english speaker too?
Voice-Ore - Small agency that can't quite figure out how to run itself. Adopted by the /vt/ Uto threads because Nabi(Uto's artist) drew two of their three girls.
VOMs - Pikamee and her sidekick, almost always has their own dedicated thread on /vt/
WACTOR - The first company to capitalize on the lucrative Spanish market. Most of their talents make tens of dollars per stream! Sometimes has a dedicated thread on /vt/ for some reason.