Why does it show a privacy warning on my settings under my Wi-Fi name?

If you examine the precise wording of the any privacy warnings, you’ll be able to determine the likely cause…

If you are concerned about iPad warnings concerning weak security, or other elements of your WiFi setup, your WiFi network may benefit from update in either settings or improved hardware...

Your iPad is no less secure today than it was prior to the update to iPadOS15. However, your iPad is now better able to [warn] bring to your attention security deficiencies of your WiFi network, iPad settings or other elements that may impact privacy.

This support page will describe the more secure (recommended) settings for WiFi:

Recommended settings for Wi-Fi routers and access points – Apple Support

It is possible that your WiFi Router is too old to be (or not capable of being) configured for more secure settings. As such, you can either configure the most secure settings that your Router will support - or replace your Router with something more advanced that provides better security configuration options. 

Whilst WPA3 is the newest standard, you should aim to use WPA2 (AES-PSK) as a minimum. Some Routers seemingly continue to support the insecure/deprecated TKIP standards - even when apparently configured for WPA2 operation; TKIP will definitely cause a security warning to appear. Be aware that if you are using a WiFi network extender, these may continue to use weaker security standards - and continue to trigger a warning.

There is a also new privacy feature included within iOS/iPadOS14/15 that hides your physical MAC Address - and instead uses a randomly selected Private MAC Address. This feature can be enabled/disabled on your iPhone/iPad for each configured WiFi Network. This feature also has bearing upon the appearance of the Weak Security notifications.

More information about this new feature can be found here:

Use private Wi-Fi addresses in iOS 14, iPadOS 14 and watchOS 7 – Apple Support

If you are unable to employ more secure security settings on your WiFi network, you might consider replacement of your WiFi network equipment, such as your WiFi Router, with more advanced equipment. However, if the router is provided by your ISP, this may not be practical proposition. A potentially cheaper and more flexible approach might be to add an additional upstream WiFi Router, of WiFi Access Point (AP) that meets the required standards.

Turning to broader Privacy issues, having updated to recent version if iOS/iPadOS15, your iPad and iPhone may now be attempting to use new services, provided by Apple, intended to mask your DNS requests. 

DNS is an unencrypted protocol that resolves hostnames (used by humans) to network IP Addresses (used by computers). As DNS requests are “in clear” (i.e., not encrypted), this traffic is often monitored by your ISP and the network operators over whose networks your internet traffic will traverse. From your DNS traffic a lot useful information can be derived about your interests and geographic location. Apple now attempts to mask your DNS traffic by encrypting this protocol.

Some broadband operators will attempt to block some types of encrypted protocols or network traffic. Where this occurs, in blocking the encrypted DNS traffic, your Apple devices automatically “fall-back” to using standard DNS lookup - and reports this to you by way of a “privacy warning” that you may see. In such circumstances your network connectivity is unaffected - but in such cases your DNS traffic is being monitored exactly as it was before you updated your devices to a more secure version of the iOS/iPadOS Operating System. As such, you may just be seeing an informational warning that some secure/encrypted protocols are being blocked either by your local WiFi network - or potentially by your internet provider.

I hope this information provides some helpful insight into ways to resolve the WiFi Security or other Privacy warnings that you might observe after updating to iPadOS14/15.