chore: rebrand project to GopherGate

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

Dockerfile

@@ -11,7 +11,7 @@ RUN go mod download
 COPY . .
 
 # Build the application
-RUN CGO_ENABLED=0 GOOS=linux go build -o llm-proxy ./cmd/llm-proxy
+RUN CGO_ENABLED=0 GOOS=linux go build -o gophergate ./cmd/gophergate
 
 # Final stage
 FROM alpine:latest
@@ -21,7 +21,7 @@ RUN apk --no-cache add ca-certificates tzdata
 WORKDIR /app
 
 # Copy the binary from the builder stage
-COPY --from=builder /app/llm-proxy .
+COPY --from=builder /app/gophergate .
 COPY --from=builder /app/static ./static
 
 # Create data directory
@@ -31,4 +31,4 @@ RUN mkdir -p /app/data
 EXPOSE 8080
 
 # Run the application
-CMD ["./llm-proxy"]
+CMD ["./gophergate"]