Hi, Elijah, I'm happy to see you are getting into the world of calculator programming. It's fun!
With your program, I can see what you are trying to do, but the calculator can't turn your human-speak into calculator speak. So we need to turn your program into something the calculator can read. I suggest you go to the intro page on this site, where you can learn everything there is to know, but for now I can at least get you started.
TI Basic cannot use user-defined variables such as the "whatsmyname" variable you described. For storing text, you'll want to use a string (the calculator has 10, Str0-Str9). So the first part of your program might look like this:
Disp "You're", Str1
Disp "Would you like a name change?"
The next part of your code is asking a yes or no question. This can be done many ways, but the simplest is probably to ask for a number, 0 or 1, and then interpret that as a yes or no. I used the prompt command, which is the simplest way for a user to type in a value that the calculator can work with. In this case, I have the prompt command store to the variable A (again, other pages on this site can give you even more info if needed):
Disp "0 for no, 1 for yes
Prompt A
Finally, we need to write code to test whether they said 0 for no or 1 for yes. This time I am using prompt to let the player store their new name, which is why it has a string variable after it instead of a number variable:
If A=1
Then
Prompt Str1
Else
Disp "Ok, fair enough."
End
One note about the Prompt Str1 line. You will have to give your answer inside quotes so that the calculator knows you're writing a word and not number variables.
So there you go, a working program (not the simplest program or the smallest in size, but it works)! When I first started I found a lot of help from the Starter Kit page, so check that out if you want to learn more. Happy programming!