I'd assume in most of the time you add, fix or change something. Typing

changelog insert --add "some new feature"

is not that big of a deal, however

changelog add "some new feature"

seems more natural.

A more complete list:

changelog add "some new feature"
changelog fix "some bug"
changelog cha[nge] "an existing feature"
changelog rm "an unnecessary thing"
changelog rem[ove] "an unnecessary thing"
chagnelog dep[recate] ""
chagnelog sec[ure] "something critical"

Note: characters in [] are optional, however I think it makes sense to add autocompletion for them. When tabbing:

changelog <TAB>
add
change
deprecate
fix
find
insert
remove
secure

looks way nicer than

changelog <TAB>
add
cha
dep
fix
find
insert
rm
sec

Contra

changelog remove is kind of ambiguous. However, since deleting the CHANGELOG.md file is not a common use-case, I think this should be fine.

One could also argue, that this adds an unnecessary amount of commands, which are already supported by changelog insert.