Details about authorized test centres can be found here:

There are a number of websites out there offering to book language tests, these are usually sites that charge you extra to do something you can do yourself. You must book tests EXCLUSIVELY with the AUTHORISED PROVIDERS listed below.

At the time of writing, the language test fee is £150 with either provider.

Language tests are only valid for two years.

The relevant date is when the application is submitted, not the date of the UKVCAS appointment.

Although the test providers also offer courses and preparation materials, most naturalisation applicants should be able to pass the language test without study or preparation.

The language test is an oral speaking and listening test, lasting around 10 minutes on average. You need to pick a topic of conversation for the test.

You need to book either: B1.1 is the same as B1

There are two more authorised providers now: Direct link to IELTS Life Skills B1 test centres: UKVI - United Kingdom
The language test for citizenship is an oral test, and it used to be a face-to-face chat with the examiner, however, ever since the centres re-opened after lockdown, it has been delivered remotely

You need to choose the computer-based test rather than the paper based one.

If you click on that option on the booking page, it takes you to another page that lists a number of options:
IELTS UKVI Registration the bottom of that page, you find:

Click image for larger version  Name:	IELTSTest.png Views:	1 Size:	42.0 KB ID:	44232

Check out the ID requirements to book and take the test.

The language test is only valid for TWO YEARS. Do not book the test until you are ready to apply for citizenship.
Before booking the test, check out if you can be exempt from it: Even if you are exempt from the language test, you may still need to sit the Life in the UK test.

Life in the UK Test