Different people do it differently. I memorise them by associating images with them either from the facts or the name. For example, Lawrie-Blum - I think of a teacher in a classroom. Boxfoldia v NGA - I think of my old headteacher (who had a similar surname) dressed as a secret agent. Douwe-Egbert makes me think of eggs.
Cut out unnecessary words. For example, Baden Delvaux v Societe Generale (omitting the rest of that stupidly long name).
For EU, I always just put it down to one word (or called it Commission v Germany on the basis that 50% of the cases are Commission v Germany). Meca-Medina. Kaur. Walrave and Koch. Jany. Genhardt. Admittedly, I did nearly entirely substantive law for my exam. There are a few long German names you need to know though IIRC.