When several instances of Bristol are running, the first one's jack client name is 'bristol', with subsequent instances appearing as 'bristol-01', 'bristol-02', etc. which is the default behaviour for multiple jack clients of the same name.
It'd be handy (for me anyway) if the emulation name were appended to the jack client name, so I'd instead see (e.g.) bristol-mini, bristol-solina and so forth in qjackctl. I assume this wouldn't be too terribly difficult to do: if I get a few moments I might even try to implement it myself.