A “burner phone” in this context is a prepaid cellular mobile phone that can be purchased and activated without any identification or through an identifying registration process.
Therefore by default, burner phones are technically anonymous. However, that state of anonymity is retained and only secure by how it was acquired.
In most conditions under proper strategic use, it’s essentially impossible to be monitored or tracked, time and vigilance notwithstanding.
There’s no personal data connected to the user that correlates to the device. Privacy is guaranteed, for a limited time / usage per phone / SIM.
Just because an ID or registration isn’t required to buy and activate a burner, it doesn’t mean that the user can not be identified or tracked.
This is why burners must be purchased with cash, never with credit cards or other identifying forms of currency. As the identity of the purchaser can be easily ascertained to the burner phone / SIM.
To further user security, have an asset that has no connection to you physically purchase the burner phone for you as a privacy redundancy.
For long-term or extended burner use, consider acquiring the phones from a diversity of sources while avoiding buying in bulk from the same places.