The garmin map for Jamaica lacks the north half of the island

Subject says it all.

I can add the missing tile, but then the map installs as “OSM generic routable” and replaces the existing “OSM generic routable”. Since for some of my work I use a map of Hispaniola that is the Haiti (or Dominican Republic) map plus the rest of the tiles needed, also installed as “OSM generic routable,” this is a problem.

One solution would be to install a downloaded map with a name I choose, but I can’t see how to do this.

Where did you download the garmin map for Jamaica from? There are lots of people offering Garmin downloads (see e.g. https://wiki.openstreetmap.org/wiki/OSM_Map_On_Garmin/Download ). You’ll need to raise the issue with whoever you downloaded it from - and of course you could try a different source to see if that has the same problem.

I downloaded it from http://garmin.openstreetmap.nl/

I reported the problem to openstreetmap.org, was basically blown off and told to take it to this forum.

I think you should enable manual selection and chose the tiles you are interested in.

If my answer didn’t help: The correct thread for questions like this is here: https://forum.openstreetmap.org/viewtopic.php?pid=772916