Change the name of your iPhone. The default name may include your actual name, which can be seen in more places than you'd think.
Wipe/reset your iPhone every now and then. There is residual data left on the phone from app/data deletion (left over databases even). A factory reset will clear this, OS updates can help as well. The "Other" section of your iPhone storage is dangerous.
Make sure the emergency feature to disable TouchID/FaceID is enabled. When turned on it kills biometrics until you put in your (hopefully unique and complex) password. Otherwise, biometrics is safer.
Don't add any mail accounts to the native iOS mail app.
Ensure that access to USB accessories while the phone is locked is turned off.
Work only on LTE and your own private Wi-Fi (your job will have very complex monitoring tools like FireEye). Disable cellular data on any apps that you won't actively be using.
Backup your iPhone to a secure location when travelling, wipe your phone and then re-build your phone using the backup upon arrival. Destroy the backup after.
Don't open any shady URLs and make sure you always update iOS. Turn on auto-update.
Security is critical on iOS as some apps have the ability to log you in or restore a session without any sort of credential check. This is despite the fact that unique device identifiers are not supposed to be used by devs.
Another thing you can do is to download apps using one Apple ID, then login again to the App Store with a different Apple ID.
The tricky thing about iOS is things are always changing, so precautions that might seem fruitless today may be critical tomorrow.