Hmm, that’s a good question! As for the Serenity name, I think it’s a title of sorts for members of the Moon Matriarchy; I have a headcanon that all Queens before and after Usagi will have Serenity or a variation of it somewhere in their title (not like Serenity IV, Serenity V and so on, but unique names like “Serenity Luna” or something).
As for Chibiusa, the name “Chibiusa” itself is just a nickname; her full name is “Usagi Small Lady Serenity” and she goes by “Small Lady” in the 30th Century; NQS, whom she considers her true mother (although Usagi is the same person it’s clear that Chibiusa sees her more as a sister), calls her that as well. Chibiusa was a nickname thought up by Mamoru to distinguish her from the regular Usagi because Chibiusa originally said her name was Usagi.
At one point in the manga (too lazy to look it up right now but it’s in the last chapter of the R arc), Chibiusa actually says she likes her nickname. So I don’t think she has any hard feelings over it!