First I must say, I don't know much about any other than the style I train in. Ryu Kyu Kobujutsu Hozon Shink Kai.

But I heared about some other styles. Yamane Ryu, Matayoshi Kobudo.

The big names I keep hearing are Matayoshi and Shinken Taira.

Are these to only styles and are there more big names that I might find interesting?

I'ld like to search a bit into the beginning and the fathers of kobudo.

Can you help me a little further?

Yamani , Matayoshi, and Ryukyu are the largest surviving kobudo systems today, however i know that there is still small systems such as Village Kobudo as taught by Hohan Soken which is still preserved.

bump

(topics like this should be stickied in case others want to add links, or more info)

recently heard of a kobujutsu system being taught in the UK called Itosu Ryu Kobudo. I think the katas that they study are primarily of ryukyu origin. I didnt find much more on them.

I recently heard of a style called 'tesshinkan'. It is trained in germany somewhere, if I understood well. Don't know anything more, maybe I can find some more info.

The Ryukyu splits in Inoue and Akamine. Tesshinkan is a version of the Akamine lineage.

BÔ – KATA
SHÛSHI-NO-KUN (SHÔ) / (DAI)
SAKUGAWA-NO-KUN (SHÔ) / (DAI)
SUEYOSHI-NO-KUN
SOEISHI-NO-KUN
SOSEKI-NO-KUN
CHÔUN-NO-KUN
CHINEN-SHIKIYANAKA-NO-KUN
YONEGAWA (YUNIGA)-NO-KUN
SEISOKO-NO-KUN
SHIROTARU-NO-KUN
TSUKEN-NO-KUN
CHATAN-YARA-NO-KUN
KONGO-NO-KUN
URASOE (URASHI)-NO-KUN
CHIKIN (TSUKEN)-SUNAKAKE-NO-KUN ( ÊKU )

SAI - KATA
CHIKIN (TSUKEN)-SHITAHAKU-NO-SAI
HAMA-HIGA-NO-SAI
CHATAN-YARA-NO-SAI
KUGUSUKU (KOJO)-NO-SAI
YAKAA-NO-SAI
TAWATA-NO-SAI
MANJI-NO-SAI

KAMA - KATA
TOZAN (TOYAMA)-NO-NICHÔ-KAMA
KANEGAWA-NO-NICHÔ-KAMA

TEKKÔ - KATA
MAEZATO-NO-TEKKÔ

TUNFA (TONFA) - KATA
HAMA-HIGA-NO-TUNFA
YARA-GUWA-NO-TUNFA

NUNCHAKU - KATA
MAEZATO-NO-NUNCHAKU
AKAMINE-NO-NUNCHAKU

TINBÊ - KATA
KANEGAWA-NO-TINBÊ

Other KATA
MAEZATO-NO-SURUJIN
KUSHAKU-NO-BÔ
SAN-SETSU-KON
YON-SHAKU-NO-BÔ

These are the kata as trained in Tesshinkan. Most of them are also in the system I train in.

Yes I study most of those as well with a few exception because we include Matayoshi Kobudo kata, as well as a few Village Kobudo kata into our curriculum as well. We also study the Nunte-bo and Eku (kai)

I train in a style of Ryu Kyu also. It's similar to the list posted above, plus or minus a few things.
I would imagine that most of the Okinawan styles are very similar with a few stylistic differences of course. This makes sense being a small island and considering much of what was taught seems to be originally derived from only a few sources.
If you're looking for historical information on Okinawan Kobudo you'll most likely find that it has not been directly connected to empty-hand arts for many generations, and that much of it is a modified form brought over from China.