Once you have chosen a name for your family you cannot change it again.
If you would like to reset/change the time, just press B until you are on the clock screen, then hold buttons A and C together, then choose the correct date/time.
The ONLY way to change the family name is to reset the Tamagotchi completely, to do this, use a pointy object (most common is a pen) and gently press the button on the back of your Tamagotchi, then select 'Reset' on the screen.
Note: Once you have restarted a Tamagotchi you can't get the previous family back.
E.g you have a family called 'Tama' with a Mametchi, Kuchipatchi and Memetchi etc.
You reset it, then set the date/time/birthday, once your new eggs have hatched you CANNOT get the 'Tama' family back.
Thats just an example, but hope i helped!
Cya!