What incognito mode is for
Private browsing helps separate a temporary browsing session from normal local history and persistent site data, depending on the browser. It is useful for local privacy on a shared device and session separation.
What the network still sees
Your traffic still uses your ordinary ISP, enterprise network or whatever network path is configured. Websites therefore still see the public IP presented by that connection unless another technology such as a VPN or proxy changes it.
Incognito versus VPN
They solve different problems. Incognito changes browser-session persistence; a VPN changes network routing and the public IP visible to destinations. Using one does not automatically provide the benefits of the other.
Check instead of guessing
Open the What Is My IP tool in a normal window and in an incognito window. On the same connection, the public IP should normally be the same.
What incognito mode actually changes
Private browsing is mainly about local browser state. It can isolate cookies, avoid saving normal browsing history after the session and reduce some persistence on the device, but it does not replace the network route used to reach websites.
When would your public IP change?
Your public IP changes when the network path changes—for example by switching from Wi-Fi to mobile data, reconnecting to a provider that assigns a different address, or routing traffic through a VPN or proxy. Opening an incognito window alone does none of those things.