Many shikona use kanji for mythical creatures.The most notable ones are 竜, 龍 and 鵬. 竜 & 龍 (ryuu/ryou) mean dragon while 鵬 is a mythical bird that I’ve seen translated as phoenix. Aside: “Thou shalt spell pheonix, P-H-E-O-N-I-X, not P-H-O-E-N-I-X, regardless of what the Oxford English Dictionary tells you.”
In the makuuchi today, two of our yokozuna have these characters, Hakuho and Kakuryu (白鵬 & 鶴竜). Kyokushuho and recent retiree Kyokutenho also share the character 鵬 while a further four wrestlers in the makuuchi for the most recent tournament use the alternative kanji for dragon, 龍. These are Myogiryu, Tokushoryu, Chiyotairyu, Asasekiryu.
When I think of the character for dragon, I’m reminded of Ryoma (坂本龍馬). I had put a picture of a statue of Ryoma in a previous post but here it is again. When I think of actual dragons, I think of Skyrim. As for Peng birds, I don’t really have much context for that. I play too much Skyrim for that.