Generally, the pharmacy keeps track of that. Even if you see that you prescribed Zantac on the 1st so that it is due on the first of next month, the patient may not fill it until the 10th. Obviously, the refill date would be the 10th. The pharmacy will know that info, and you will not, and they will never call you to get your info as it really would not be helpful.
As Marty says, making sure AC has your refill turned on is helpful. I hate to say it, but I would prescribe Zantac and tell the patient they have refills. They can fill them late (I think up to a certain point) just not too early. So, I find I just stay out of it and let the patient and the pharmacy figure it out.
Don't worry, the patient will likely call you at 7 am on a Saturday asking for a refill. Even worse, probably of a controlled substance.