1. Re-install whatsapp on the same phone and same SIM : you have to go through the entire setup process again. You're asked for your phone number, whatsapp sends a sms to that number to confirm. If you had previous backup of chats, it restores that.
2. Insert SIM into a new phone, without whatsapp previously installed: Same as 1.
3. Change SIM in the same phone and whatsapp previously installed: Nothing changes. Whatsapp runs using your previous number and that is displayed to all the contacts. On re-installing, 1. is repeated.
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I have tried some of the cases:
1. Re-install whatsapp on the same phone and same SIM : you have to go through the entire setup process again. You're asked for your phone number, whatsapp sends a sms to that number to confirm. If you had previous backup of chats, it restores that.
2. Insert SIM into a new phone, without whatsapp previously installed: Same as 1.
3. Change SIM in the same phone and whatsapp previously installed: Nothing changes. Whatsapp runs using your previous number and that is displayed to all the contacts. On re-installing, 1. is repeated.