fix: use cookie name as storage key (#730)

* fix: use cookie name as storage key

* chore: add changeset

Author: kangmingtay

.changeset/six-moles-perform.md

@@ -0,0 +1,5 @@
+---
+'@supabase/ssr': minor
+---
+
+use custom cookie name set

packages/ssr/src/createServerClient.ts

@@ -38,6 +38,14 @@ export function createServerClient<
 
 	const { cookies, cookieOptions, ...userDefinedClientOptions } = options;
 
+	// use the cookie name as the storageKey value if it's set
+	if (cookieOptions?.name) {
+		userDefinedClientOptions.auth = {
+			...userDefinedClientOptions.auth,
+			storageKey: cookieOptions.name
+		};
+	}
+
 	const cookieClientOptions = {
 		global: {
 			headers: {