[vid]

Still her, the reigning monarch will remain in that role until her death. However, they've already got an obverse with Charles' portrait for the coins ready to go so the transition happens fairly swiftly. The last time there was a transition, they didn't start issuing coinage with the Queen's image on it until over a year and a half after her reign. Similar for when King George VI took over in 1936. The redesign of the $20 bill in Canada won't happen until after the Queen dies, and apparently as the UK shifts to polymer, they've already got versions of each note with Charles on them ready to go.

He likely won't use the name King Charles (look up the previous two to get a sense of why), his full name is Charles Phillip Arthur George. He might go with Phillip II to honour his father (the first King Phillip was monarch of Spain and ruled briefly prior to Elizabeth I's reign), or King George VII to honour his grandfather. King Arthur, due to the mythology of the name, is highly unlikely. From what I've seen, King George VII is the most likely title he will use. William will likely rule as King William IV.