Update parameter-names.mdx based on issue #266

Author: kgowru

fern/products/openapi-def/pages/extensions/parameter-names.mdx

@@ -1,16 +1,19 @@
 ---
 title: Customize parameter names
-description: Use `x-fern-parameter-name` to customize query parameter, header and path parameter naming.
+description: Use extensions to customize parameter naming and behavior in your generated SDKs.
 ---
 
 <Note>
-  The `x-fern-parameter-name` extension allows you to customize the variable names of parameters in your generated SDKs.
+  Extensions allow you to customize how parameters are handled in your generated SDKs. This includes renaming parameters and injecting values via constructors.
 </Note>
 
-## Headers
+## Parameter naming with x-fern-parameter-name
 
-In the example below, the header `X-API-Version` is renamed to `version` in the
-generated SDK. The rename makes the SDK more human readable.
+Use `x-fern-parameter-name` to customize variable names for parameters in your generated SDKs.
+
+### Headers
+
+Rename header parameters to make them more idiomatic in your SDK:
 
 ```yaml {8}
 paths:
@@ -26,10 +29,9 @@ paths:
           required: true
 ```
 
-## Query parameters
+### Query parameters 
 
-In the example below, the query parameter `q` is renamed to `search_terms` in the
-generated SDK. The rename makes the parameter more approachable for end users.
+Make query parameter names more descriptive and user-friendly:
 
 ```yaml {8}
 paths:
@@ -45,10 +47,9 @@ paths:
           required: false
 ```
 
-## Path parameters
+### Path parameters
 
-In the example below, the path parameter `userId` is renamed to `id` in the
-generated SDK. The rename makes the SDK less verbose.
+Simplify verbose path parameter names:
 
 ```yaml {8}
 paths:
@@ -63,3 +64,40 @@ paths:
             type: string
           required: false
 ```
+
+## Constructor Variables with x-fern-sdk-variables
+
+Use `x-fern-sdk-variables` to define variables that can be set once in the client constructor and automatically injected into requests.
+
+```yaml
+components:
+  x-fern-sdk-variables:
+    project_id:
+      type: string
+      description: "The ID of the project"
+      pattern: "^proj_[a-zA-Z0-9]+$"
+```
+
+This variable can then be referenced in path parameters:
+
+```yaml
+paths:
+  "/v1/connect/{project_id}/accounts":
+    parameters:
+      - name: project_id
+        in: path
+        required: true
+        schema:
+          type: string
+          pattern: "^proj_[a-zA-Z0-9]+$"
+        x-fern-sdk-variable: project_id
+```
+
+The generated SDK will now:
+1. Accept the `project_id` in the client constructor
+2. Automatically inject it into requests that require it
+3. Free users from having to pass it on every request
+
+<Note>
+  SDK variables are currently supported in TypeScript and Python SDKs (version 4.24.0+).
+</Note>