The second issue can be addressed by renaming the map with JaVaWa GMTK (the map on the computer) or with JaVaWa Device Manager (the map on the device), but these programs cannot solve the third issue.
The solution is joining multiple maps to a single one, and eliminating the overlapping segments. This can be done with OSM Combiner, and you can rename the map at the same time.
Note: OSM Combiner is designed exclusively for the maps from garmin.openstreetmap.nl and OpenFietsMap.nl. It has not been tested with other free maps, but it should work with any mkgmap-generated map. With non-free maps it certainly doesn't work.
OSM Combiner requires Java version 7 or higher on your computer.
Windows users can download Java here. If you have a 64-bit version of Windows, get the 64-bit version of Java.
On the Mac it depends on the version of OS X. When you have Leopard or Snow Leopard and you run Software-update regularly you will have the right version on your Mac.
Users of (Mountain) Lion can get Java here: http://support.apple.com/kb/DL1421, or the one from the Java website.
The version of Java under Tiger is unfortunately not the right one, but on this site Tiger users can acquire a working alternative.
To use OSM Combiner you have to download the desired maps first. garmin.openstreetmap.nl is offering several downloads; for OSM Combiner you need the file whose name ends in
_tiles.zip or the file whose name ends in
osm_generic_tiles.zip). Extracting the zip files is not necessary.
Preferably use the first type (
_tiles.zip), because these contain additional files to create the overview map. Without those extra files the overview map will be an empty rectangle; not so pretty when you zoom out further in Basecamp or MapSource. On the device it doesn't matter, because the overview map isn't used there.
It is strongly recommended to download all desired maps consecutively. This is because with every update of the maps on the server of garmin.openstreetmap.nl the numbering of the map segments may change, so that the overlapping segment IDs of a previous downloaded map match up with those of a new one. It is essential for OSM Combiner that the IDs of the overlapping segments match.
You can also use other free maps, whether in the form of a combined .img file meant for devices (usually named gmapsupp.img) or as separate map segments. OSM Combiner can handle archives containing these files in .zip or .7z format.
OSM Combiner can install the map right away when it is finished, but you have the option to install the map later when you want to move it first.
Under Windows the result can be found in a subfolder (with the specified name for the map) of the folder you chose at the beginning. Put this folder in a location of your choice, and install the map with
install.exe. You can also convert the map to the .gmap format with JaVaWa MapConverter.
Uninstalling the map can be done with
uninstall.exe, through Windows Control Panel or with JaVaWa GMTK.
On the Mac the map is automatically converted to the .gmap format. The result can be found in the folder you chose at the beginning. When installing a copy of the map will be made; after installation you can remove the folder you chose at the beginning.
You can install, uninstall or move the map with JaVaWa GMTK.
It may be that there isn't allocated sufficient memory to mkgmap; in that case you have to adjust the value yourself. The type of operating system and the amount of physical memory determines the maximum you can set.
Generally speaking, keep it lower than about 75 - 80% of the amount of memory of your computer. If your OS is 32-bit, don't set it higher than 1400 MB. It may take some experimenting; when mkgmap doesn't succeed in creating the necessary files, you can always try again with another value.
Creating a gmapsupp.img requires a lot of additional memory, so don't check that option unless you really need it.
The dialog also shows some information about Java: the version number, and whether it is a 64-bit version or not.
The idea for OSM Combiner is based on the command line tool OSM-Combi of OpenFietsMap.
OSM Combiner uses the applications mkgmap and GMapTool; the Windows version of OSM Combiner also uses 7-zip and NSIS, and the Mac OS X version uses the command line version of The Unarchiver.