Notes:

Okay, this is going to be a lengthy explanation, so bear with me.

In Kamen Rider Decade, Tsukasa Kadoya (Decade) nicknames Natsumi Hikari (who later becomes Kamen Rider Kivala) "Natsumikan," a double pun on both the -kun honorific and the amanatsu fruit, also known as the natsumikan, which is a type of orange.

S.I.C. Hero Saga takes this pun and runs with it. In the OOO story (which introduced OOO's Final Form Ride and Super Rising Ultimate Kuuga), Natsumi becomes a female Gaim by infusing a blank Lockseed with a combination of Kivala's power (hence the bat on the helmet) and Gaim's Orange Arms, creating Natsumikan Arms!

You got all that? Cause this will be on the test.