Im not sure LLM prompt alone will help, you can give elevenlabs pronunciation via CMU or IPA syntaxes
https://elevenlabs.io/docs/best-practices/prompting/controls#pronunciation
This might need custom LLM approach, so you can detect names, have dictionary of names with their pronunciation to replace names with pronunciation in message you send to TTS. Although Im not sure it would work, you can try hardcoding few and see how it works.