There are some groupings in the periodic table, and using them would definitely help you learn the connections and make it easier to remember. However, even if some elements are have “logically derivable” names (I’m not sure any do, honestly), some definitely do not, since they were named after the person who discovered the element, a country, or random other name. So you can get part of the way with connections, for example Berkelium is 97 and Californium is 98, easy to remember together. But as far as I know, if you forget Curium is 96, there isn’t any way to get to that from other information.