Your GPS will recognize any map file with an .img extension. This should also work with a map on a card. If you connect the GPS itself to your computer, then use Basecamp/MapInstall to send maps, the software should be able to figure this out all by itself and will assign unique names to each map.
However, if you have the card in a reader then the software won't know what kind of GPS you have. Older Garmin handhelds would only recognize a single file name - gmapsupp.img. So the software will fall back to the lowest common denominator and always name a map gmapsupp.img if the card is in a reader.
There should be several solutions. The easiest is probably just to put the card in the GPS and connect it to your computer, then let MapInstall figure out the rest.
Another possibility is to copy the file GarminDevice.xml from the GPS to the card. This file is used to describe the GPS capabilities to MapInstall. So if you copy it to a card, MapInstall will think the card actually *is* your GPS. It should then assign unique map names.
Then there's the brute force approach. After sending the first map, manually change the name form gmapsupp.img to WhatEverYouLike.img. Then send another map and repeat. This will also work with Mapsource.
Personally, I rarely use Garmin's new software like Basecamp and MapInstall. So I use the brute force approach with Mapsource most of the time.
