I am thinking of doing a map based on an old TV show (began in 1965 and ended in 1971). Are there any issues with using the name and maybe a picture on my map?
Unless you have produced the picture yourself, you will need to get permission from the copyright holder of the picture. As far as the name goes, it might depend on the name, but most TV series names would be either under copyright or trademark. If you can get permission from the intellectual property owner(s) (as was done for the Discworld map), then you're fine, but otherwise, Conquer Club will not be interested in developing or using such a map.
Hm, yes, the idea is good. You could do it by changing the names a bit here and there, so that you won't be using material from the show, but it would still be sort of recognizable where it is taking influence from.