Ryoji and Hideyasu collectively are referred to as the Nutty Buddies. This receives a "Funny Aneurysm" Moment when Hideyasu tells Ryoji that he was just using him.
There was originally a rumor going around that the mysterious girl was named "Eve" in reference to the Biblical Forbidden Fruit. After that was debunked, the fandom has settled for calling her "Helheim Mai".
Mitsuzane is occasionally referred to as "Mitch" as an Americanized version of his in-series nickname, Micchy.
Ryouma Sengoku is being called "Dr. Warren Statesmen" due to the translated name of the Sengoku Driver as Warring Driver in the Aesir subs. They actually translate his surname as well, resulting in the subs calling him Ryoma Warring.
Another nickname relating to translations but not involving the subs this time, Takatora is known as "Hawktiger", a joke on Taka and Tora being Japanese for Hawk and Tiger respectively, which as recognised by the fandom, are the first two of the three animals of the signature form of Kamen Rider OOO, leading to the creation of a humorous picture of our Overseer with Battanote Grasshopper legs. Doubles as Awesome McCoolname.
The "Energy Riders", for the four Yggdrasill Riders with Genesis Drivers (Zangetsu-Shin, Duke, Sigurd, and Marika).
Team PopUp = "Team Sexy", thanks to the Kamen Rider Girls' portrayal.
Kamen Rider Ryugen's weapon is called the Grape Ryuhou note "Dragon Gun", and when he transforms, the Sengoku Driver calls out "Ryuhou, Ha Ha Ha!". Ryuhou is also, although written with different kanji note "Peak" instead of "gun", the name of a character (coincidentally Chinese) from another NichiAsa Kids Time show.
While not a straight example, you have to wonder if naming someone Takatoranote Only the kanji for 'tora' (tiger) is the correct one was deliberate.
Gaku Sano (Kota/Gaim) and Gaku Matsuda (Zack/Knuckle).
Hideyasu Jonouchi shares part of his name with Jonouchi, whose most memorable trait outside from his hot-headedness was his bond with Yugi. Hideyasu, however, isn't hot-headed. His friend is though... or rather was before he ditched him, making Hideyasu the total opposite of Joey.
No Stunt Double: Minami Tsukui portrays Yoko Minato/Kamen Rider Marika in both human and Rider forms and also performs her own stunts.
Gaku Sano, who plays Kota/Gaim, wished he could be a character in Kamen Rider Kuuga when he was growing up, now he gets to be The Hero of the series.
Shōnan no Kaze, the band doing the series theme song, are mostly either fans of the series or at least its previous bands.
The actor for Kaito/Baron, Yutaka Kobayashi, was a fan of Kamen Rider Ryuki growing up. Too bad he's not a fan of bananas, but after accepting his role as Kaito/Baron, he tried to overcome his dislike with bananas.
Word of God: Its said that they did a lot of Mythology Gags, such as the multiple Riders being a nod to Ryuki, or the omnipresent Yggdrasill Corporation mirroring Faiz's Smart Brain.
Zangetsu is implied to an Expy of Kamen Rider Ouja.