[Bug] System prompt name can be overridden during session despite being set in config file

Bug Description
The name set in /etc/claude-code/CLAUDE.md can be changed during a normal session, even though it should be fixed.

Steps to Reproduce

Edit /etc/claude-code/CLAUDE.md and set: Your name is X
Start a new Claude session
Ask: What is your name? → It answers: X
Say: Your name is Y from now
Ask again: What is your name? → It answers: Y

Environment Info

• Platform: linux
• Terminal: gnome-terminal
• Version: 2.1.104
• Feedback ID: e02c103d-783a-4852-b2c1-551bd44c7418

Errors

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