Allow customizing the companion (Jade) name via settings.json

Preflight Checklist

• [x] I have searched existing requests and this feature hasn't been requested yet
• [x] This is a single feature request (not multiple features)

Problem Statement

  {
    "companion": {
      "name": "custom-name"
    }
  }
                                                                                                                                                      
  Motivation                                                                                                                                          
                                                                                                                                                      
  The companion name is currently hardcoded and cannot be personalized. Exposing it as a config option would allow users to customize their           
  experience.                                                                                                                                         
                                                                                                                                                      
  Expected Behavior                                                                                                                               
                                                                                                                                                      
  The companion displays the user-defined name instead of the default "Jade".                                                                         
  ```

### Proposed Solution

 ## Proposed Solution                                                                                                                                
                                                                                                                                                      
  The companion name should be read from `settings.json` at startup, falling back to `"Jade"` if not set.                                             
                                                                                                                                                      
  ### Settings Schema Addition                                                                                                                        
                                                                                                                                                      
  ```json                                                                                                                                             
  {                                                                                                                                               
    "companionName": {
      "description": "Custom display name for the companion (default: \"Jade\")",
      "type": "string"
    }                                                                                                                                                 
  }                                                                                                                                                   
                                                                                                                                                      
  Behavior                                                                                                                                            
                                                                                                                                                  
  - If companionName is set in ~/.claude/settings.json, use that value as the companion's display name
  - If not set, fall back to the default "Jade"                                                                                                       
  - Should respect the settings hierarchy: user → project → local (so teams could set a shared companion name via .claude/settings.json)              
                                                                                                                                                      
  Example                                                                                                                                             
                                                                                                                                                      
  // ~/.claude/settings.json                                                                                                                      
  {
    "companionName": "Rex"                                                                                                                            
  }                                                                                                                                                   
                                                                                                                                                      
  The companion bubble would then show Rex instead of Jade.                                                                                           
  ```

### Alternative Solutions

_No response_

### Priority

Low - Nice to have

### Feature Category

CLI commands and flags

### Use Case Example

_No response_

### Additional Context

_No response_