I've considered using aliases for the above because adding the periods might make it hard for people used to the old spelling to find these chartags, but since Opera only has 36 posts while Mr. C.B. has 8, and the most prominent English wikia has it spelled the same as the official spellings, it's probably unnecessary.
Bunch of alternate spellings
English Wikipedia and some horse racing newspapers spell the names of the real life horses as "T M Opera O" and "Mr C B", without the periods, but this use is mostly confined to the real-life horses. Think this is probably an in-house style format or something for the newspapers with Wikipedia following suit when they used those articles as their sources.
There's another far more common alternate spelling for Opera, as TM Opera O, which is used for the Umamusume character on Tvtropes and Gametora, and also used in discussions on forums (both Japanese and English). The Umamusume English Twitter also uses this spelling (along with T.M. Opera O). This spelling is also used for the real-life horse (being more common then the spaced variant), including on the Japanese wikipedia article.
Mr. C.B. has three common alternate spellings (more common than Mr C B), as Mr.C.B. (no spaces) Mr.CB (no spaces and no periods on initials) and Mr. CB. Mr.CB is the one that pops up most often in Japanese discussions (and is also used for the namesake soccer manga). Mr.C.B. gets used mostly only for the real-life horse (Japanese wikipedia article and some horse fan wikis/databases).
TL;DR: There's a lot of alternate spellings for the above two Umamusume characters but I don't think we need utility aliases yet. Though things might change in the future depending on how popular the Gametora/Tvtropes spellings become. A TM_Opera_O alias might be useful, especially since the official Umamusume English Twitter account also uses this spelling sometimes.
Trivia: The names are supposed to be initials, which is why they have the periods. T.M. is short for "Takezono Masatsugu" (owner of the real-life horse), while C.B. is short for "Chigira Bokujou" (name of the breeding farm for the RL horse).