Was using CraftTweaker and the zenscript line

<xtones:zome:12>.displayName = "Base Alchemical Beacon (Active)";

to change the names of an xtone block. However it ended up changing all of the Zome blocks instead of just the red one of meta 12. displayName seems to work correctly with other items such as Thermal Foundation ingots, or wood planks.

Yup

Is it possible to make it so that blocks of different colors/metas have different names in xtones?

Nope