If you SMS text someone, how much more information will they know about you?

To answer the question yourself I suggest you to look around for some old SDKs like Siemens included to its cellular phones (S50?) with some tools i.e. something like SMS Builder to test your apps.

• If you publish you mobile number in a directory such as Spokeo they can look you up

• If you use Telegram, the other person will be able to see your public name. Your last seen online time could be retrieved either precisely or imprecisely depending on your privacy settings - this information cannot be hidden completely. Telegram will always tell anyone whether you're currently online (using the app) or not. You can make your profile photo visible only for your contacts.

• If you use WhatsApp you can hide your last seen info and profile photo completely from everyone. Your public name can also be seen by anyone regardless.

• It's trivial to find out what your cellular operator is and in many cases it's not difficult to pinpoint the location where the SIM card was sold to you.