Phantom does not have a traditional log out feature. Because your wallet is stored locally on your device and protected by your credentials, there is no session to sign out of the way you would with a web app or exchange account.
How to secure your wallet instead
Browser extension
The extension is protected by a password. You can lock it immediately by going to Settings → Lock Wallet, or set it to lock automatically after a period of inactivity in Settings → Security & Privacy → Auto-Lock Timer.
Mobile app
The app locks automatically when you close it and requires Face ID, fingerprint, or your device passcode to re-open. If you created your wallet with Google or Apple, it is also protected by your four-digit PIN. You can adjust the auto-lock timer in Settings → Security & Privacy → Auto-Lock. If you need to reset your PIN, go to Settings → Security & Privacy → Reset PIN.
If you want to remove the wallet from your device entirely
If you want to ensure no one can access your wallet on a specific device, you can reset the app. This removes all wallet data from the device. See Reset Phantom for instructions.