I use `on-connection`, as it is called once the repl has been started, when we need to connect to the repl.  I suppose what it is really doing is providing (or modifying) the endpoint to connect to.  So maybe:

* `nrepl-endpoint`
* `nrepl-connection-endpoint`

Note that this is in `nrepl-client.el` so should not have a jack-in specific name, in my opinion.