Admittedly, it was in the late 40’s an early 50’s me & my siblings were required to write to our Grandma.
The address used was:
Grandma
Town, Tx
No zip codes in those day of course.
She got the letters.
I think they also got the clue from the return address who’s Grandma it was supposed to go to.
Also, of all the Grandmothers in that town, she was “The Grandma.”