TL;DR: There is no way to be completely anonymous and use a SIM card, except for a very short amount of time as is the case with a "burner" phone.
Background: The question has come up a few times: "If I transfer my old SIM card (phone number) to a privacy phone, will Big Tech still know who I am?". Or "Can I be truly anonymous while using a SIM card?". The answer is a bit tricky, and is worth a closer look.
Your existing phone number, if moved to a privacy phone via the SIM card, is a way to fingerprint the device, but only by the cellular carrier. Google, the hardware manufacturers (Samsung, Huawei, Motorola), and app developers are all locked out. They do not have direct access to the phone's IMEI, serial number, SIM number, or anything that can ID the phone. Only when a user installs an app and gives certain permissions will they have an opportunity to collect information again. So for example, take a degoogled Pixel privacy phone out of the box with a SIM card, the only organization that can identify you is the cellular carrier (and by proxy gov't agencies) and the only thing they can easily extract is location data, unencrypted phone calls, and SMS messages.
Worst case scenario on a privacy phone where a user is being targeted, a gov't agency or well-funded organization could embed spyware such as Pegasus on the device, making it easy to collect personal data. But this is highly unlikely for the ordinary user.
Let's discuss a few configurations for making voice calls, and the affect on privacy and anonymity.
- Use a SIM, and accept that the cellular carrier knows user identity - This is the least anonymous option but we often compromise and accept that a carrier (and by proxy gov't agencies) will know our identity. Also note that obtaining a new SIM (with a different telephone number) when you first purchase a privacy phone will still allow the carrier to identify you. However, using a SIM is a viable option for the ordinary person. Anyone with a relatively low threat level can keep 99% of bad actors out of their lives by practicing good OpSec while using the phone. Keep in mind unencrypted cellular calls, SMS messages, and location data when dialing 911 is visible by the carrier.
- Use a SIM with data-only plan - This option significantly reduces data collection by the carrier. Pay for a data-only plan (no calls or texting). Always use a VPN. Use a VoIP service from Viber or Ooma to make phone calls. Use secure messaging apps like Signal instead of SMS texting. The carrier will know your identity, but they'll have very little, if any data to collect.
- No SIM, use W-Fi and apps like Signal to make encrypted voice calls - This in theory is the most private/anonymous option and requires discipline to only communicate using E2E encrypted voice/chat apps. The challenge will be to get all friends and family to use Signal (or similar app). Then what about calling an electrician or plumber? Ordering take-out? Maybe that's where a landline or second smartphone comes in handy.
- Obtain a "burner phone" / SIM card anonymously - This option requires more effort up front and there is no guarantee it will work. At least in the United States, one can still purchase a phone plan (SIM included) from a major retail store using cash (or online using gift cards and guest checkout). During registration with the carrier, a pseudonym is used instead of a real name, and temporary mailing address, and email address are given. In some cases, registration of the phone does not require any personal information. Once signed up, the monthly phone bill is paid with gift cards. So in theory, the carrier doesn't know the users' real identity. Another version of this option is to purchase the phone plan and a "Burner Phone", or throw-away flip phone. But a word of caution, this method is short lived. The longer one uses the device the more likely the user's identity will be known.
There may be another option or two, but you get the idea. There is no easy way to be completely anonymous and use a SIM card. Which configuration you choose depends on your threat level and how much personal information you're willing to share. The right answer is what you say is right for you.