You should have you're "my_guess" as an integer instead of a string. You also have an endif after "Input "Guess: ",my_guess$"
that souldn't be there.
Here's your fixed code:
_GameStart:
CLS
Print "I'm guessing of a number between 1 and 10. Can you guess which number ",name$;"?"
Randomize (Timer())
MyRandomNumber=RND (10)
Input "Guess: ",my_guess
If my_guess > MyRandomNumber
Print "You guessed too high. Try again ",name$;"."
wait 1000
Goto _GameStart
Endif
If my_guess < MyRandomNumber
Print "You guessed too high. Try again ",name$;"."
wait 1000
Goto _GameStart
Endif
If my_guess = MyRandomNumber
Print " You guessed correct!"
Print "Press the Spacebar to continue"
Endif
I added the waits in there so it doesn't go awway in an instant.