chore: rebrand project to GopherGate

Updated all naming from LLM Proxy to GopherGate. Implemented new CSS-based branding and updated Go module/binary naming.

deployment.md

@@ -1,6 +1,6 @@
 # Deployment Guide (Go)
 
-This guide covers deploying the Go-based LLM Proxy Gateway.
+This guide covers deploying the Go-based GopherGate.
 
 ## Environment Setup
 
@@ -18,12 +18,12 @@ This guide covers deploying the Go-based LLM Proxy Gateway.
 
 ### 1. Build
 ```bash
-go build -o llm-proxy ./cmd/llm-proxy
+go build -o gophergate ./cmd/gophergate
 ```
 
 ### 2. Run
 ```bash
-./llm-proxy
+./gophergate
 ```
 
 ## Docker Deployment
@@ -32,17 +32,17 @@ The project includes a multi-stage `Dockerfile` for minimal image size.
 
 ### 1. Build Image
 ```bash
-docker build -t llm-proxy .
+docker build -t gophergate .
 ```
 
 ### 2. Run Container
 ```bash
 docker run -d \
-  --name llm-proxy \
+  --name gophergate \
   -p 8080:8080 \
   -v $(pwd)/data:/app/data \
   --env-file .env \
-  llm-proxy
+  gophergate
 ```
 
 ## Production Considerations