Yes. For open models, “model and version” has to mean more than a name like llama3:8b, because local tags can be repointed and one name can cover several quantizations. What I’d record per run:
On standards: the OpenTelemetry GenAI semantic conventions define agent and tool-execution spans and attributes such as gen_ai.request.model, gen_ai.response.model, gen_ai.tool.call.id and token usage. They’re still marked Development, so pin the version you emit. For audit purposes, write the log to append-only storage that the agent’s own credentials can’t modify or delete.