[BUG] session started with `--name` CLI flag does not show the session name in the top right corner of the prompt box

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?

As 2.1.75, when the session name is set via /rename command, I can see the top-right label in the prompt box:

<img width="712" height="147" alt="Image" src="https://github.com/user-attachments/assets/a2de322c-2b53-4bed-a806-b371e15875be" />

_BUT_ when I start a session with --name CLI flag (which is added in 2.1.76), it the label doesn't appear.

What Should Happen?

The session name should be displayed regardless of how the session name is set.

Error Messages/Logs

Steps to Reproduce

1. Start a session with claude --name foobar
2. "foobar" is not displayed in the top right corner.

Claude Model

None

Is this a regression?

No, this never worked

Last Working Version

_No response_

Claude Code Version

2.1.76

Platform

Anthropic API

Operating System

macOS

Terminal/Shell

iTerm2

Additional Information

_No response_