The other alternative(s) which I would recommend over the session_name is changing the session's save path (do it in a global file used prior to anything else), and using a database instead. Both of these eliminate the possibility of conflict, assuming they are both configured differently.
Lately I've learned more about the sessions when using the
save handler. Its definitely easier to use than my old manual db sessions and a lot less code overall, but I had to write the encoder and decoders for the serialized data since PHP doesn't really have a built in way of doing it (and I don't pull from the session superglobal itself). So that did take a bit of work. If you don't need to split up the data, than that won't be necessary, just a blob type would do.