Im on Fabric for 1.20.1 and its just not displaying the heads
https://github.com/dzwdz/chat_heads/assets/72741679/4ff2a5a2-c7fb-4e77-8442-2093c62c6030

First of all, are you sure you installed the Fabric version of Chat Heads, not the Forge one?

Do the heads appear in singleplayer?
If so: Try changing Chat Heads' sender detection settings to "Heuristic Only", some servers require that. (You need Mod Menu and Cloth Config API to change the settings).
If not: What other mods have you installed?

it´s not working for me either in single player
https://github.com/dzwdz/chat_heads/assets/72741679/2beefbd7-c6cb-405b-90df-929d1f0a9dbb
these mods are installed and they work

https://github.com/dzwdz/chat_heads/assets/72741679/cff81f55-2e0a-4ea3-8ac9-038d867c9900
and these settings still not working in single or multiplayer

Ah, it's OptiFine yet again.

As with #54, #55:
We can't support OptiFine as it's closed source. Use Sodium and co instead. Here's a good list of alternatives.