Haven is just a 'port' - I cant think of a place called Haven but there is eg Rockhaven, Newhaven etc (maybe Haven is methaphoric)
Smith although the most common English name is actually reasonably uncommon on the Island so the IGI maight actually be more use than you would expect! - the name Evander I have never seen before (native Manx seldom used two Christian names at this time unless they had English connections).
1819 is unfortuneately the year before the act requiring ships passenger manifests to be lodged came into force - However you may find out more by looking at Liverpool departures/registered shipping to see if the ship is noted (most sailings to NY would be from Liverpool - or London)