The iceman nickname wasn't used for Kuklinsky in the mob. It was during media attention for his claimed body count of 200+ as a serial killer and mob hitman.

Jack the Ripper has nothing on Kuklinski, but people can remember both.

Fellows was in a gang in the UK... That was his nickname in the gang in the UK.

There's a vast ocean betwixt the states and England. While it's true that people can remember both names, it's far more likely that, in the UK, they'll remember the names of those closer to home - of the likes of Harold Shipman.

It could also be that the UK gang knew they were reusing a name, and considered that reuse part of their opsec. If anybody ever overheard the wrong conversation, they'd hear the name of a known and convicted hitman, which might lead them to believe the discussion they overheard was more mundane than they might otherwise have thought.

For instance, battle tanks are called "tanks" today because when they were being developed by the British during WWI, they wanted a word that would obscure meaning to anybody who happened to overhear the word. They were originally called "Caterpillar Machine Gun Destroyers or Land Cruisers", which was very descriptive, so they decided to call them "water containers" instead. W.C. was considered an unsuitable initialism though, so they so they settled on "tank" as in "water tank". That name stuck so well, today most people never suspect it was originally meant to obscure meaning. But at the time, any german spy who overheard the wrong conversation would think the british were discussing a method of transporting water.