[BUG] Session name set via /rename does not persist across /clear

Preflight Checklist

• [x] I have searched existing issues and this hasn't been reported yet
• [x] This is a single bug report (please file separate reports for different bugs)
• [x] I am using the latest version of Claude Code

What's Wrong?

### Problem

When you rename a session using /rename, the name is lost after
running /clear. The session reverts to its auto-generated name.

Why it matters

Users who organize sessions by name (e.g., naming after a feature
branch or task) lose that context after /clear. This makes /resume
harder to navigate — the meaningful name is gone, replaced by a
random slug.

This also makes it impossible to auto-name sessions via hooks. A
SessionStart hook can inject context suggesting a name, but since
/rename doesn't stick across /clear, the name is effectively
ephemeral.

Workaround

Starting the session with claude --name "My Feature" does persist
across /clear, but this requires knowing the name at launch time and
can't be used for mid-session renames.

Suggested fix

/clear should preserve the session name. The name is a session-level
property, not a conversation-level one.

What Should Happen?

The session name set via /rename should persist across /clear, since
/clear resets the conversation context but stays in the same
session.

Error Messages/Logs

Steps to Reproduce

1. Start a Claude Code session
2. Run /rename My Feature
3. Confirm the name shows in the terminal title / session list
4. Run /clear
5. The session name reverts to the auto-generated slug

Claude Model

Opus

Is this a regression?

I don't know

Last Working Version

_No response_

Claude Code Version

v2.1.86

Platform

Anthropic API

Operating System

Ubuntu/Debian Linux

Terminal/Shell

Other

Additional Information

_No response_