Allow setting session name from within prompt text for background agents

Feature Request

Is your feature request related to a problem?

When spawning background agents (e.g. via Claude Agents view or programmatically), there's no way to define a custom session name from within the prompt itself. Currently the only options are:

1. claude --bg --name "XXX" "prompt" — requires setting it at the shell level
2. Ctrl+R in the agents view — manual rename after the fact

This means if you're dispatching agents from within a Claude session (or from workflows/scripts that don't have direct access to the --name flag), all sessions get auto-generated names from the prompt text, making it hard to identify them at a glance — especially when working across multiple repos/branches.

Describe the solution you'd like

Support a directive in the prompt text that sets the session name automatically, e.g.:

# name: e2emon/feature-otel-metrics

Investigate the flaky SettingsChangeDetector test and fix it.

Or alternatively a frontmatter-style header:

---
name: e2emon/feature-otel-metrics
---

Investigate the flaky SettingsChangeDetector test and fix it.

This would allow users to label background agents with meaningful identifiers (repo, branch, task) directly from the prompt — without needing shell-level access to --name.

Describe alternatives you've considered

• Using --name at the CLI level (not always accessible, e.g. when dispatching from within a session)
• Manually renaming with Ctrl+R (doesn't scale when running many parallel agents)
• Encoding context in the first line of the prompt (relies on auto-naming heuristics, often gets truncated)

Additional context

This would be especially useful for users who:

• Run many parallel background agents across different repos/branches
• Use workflows or automation that spawns agents
• Want to quickly identify agents by project/branch in the agents overview