There is a relative new feature of tmux that offers what you are looking for here: command aliases.
Command aliases are different from the short alias of each command (such as lsw for list-windows). Command aliases are defined with the command-alias server option. This is an array option where each entry has a number.
The default has a few settings for convenience and a few for backwards compatibility:
$ tmux show -s command-alias
command-alias[0] split-pane=split-window
command-alias[1] splitp=split-window
command-alias[2] "server-info=show-messages -JT"
command-alias[3] "info=show-messages -JT"
command-alias[4] "choose-window=choose-tree -w"
command-alias[5] "choose-session=choose-tree -s"
Taking command-alias[4] as an example, this means that the choose-window command is expanded to choose-tree -w.
A custom command alias is added by adding a new index to the array. Because the defaults start at index 0, it is best to use higher numbers for additional command aliases:
:set -s command-alias[100] 'sv=splitw -v'
This option makes sv the same as splitw -v:
:sv
Any subsequent flags or arguments given to the entered command are appended to the replaced command. This is the same as splitw -v -d:
:sv -d