surname, kill, destroy
刘 centers on violent removal: killing or destroying. The surname sense is a proper noun application of the same character.
刘 is a character of Chinese origin, combining 文 (writing, pattern) and 刂 (knife). The exact historical development is uncertain, but it likely originally depicted a cutting or killing action, with 文 possibly contributing a phonetic element.
The left side 文 looks like a patterned target, and the right side 刂 is a knife. Imagine a knife striking a marked target to destroy it.
For リュウ, picture a deadly duel where one warrior kills another: duel -> リュウ, and the knife 刂 strikes the marked target 文.