So I've noticed that a few DS3231/DS3232 RTC modules you buy off the internet have a I2C EEPROM chip on them. Why? The DS3232 has SRAM already, and a rechargeable battery. The DS3231 doesn't need storage if it has a rechargeable battery on it does it?
So do I need a EEPROM chip if I'm building my own custom RTC with a DS3232?
No. The EEPROM is just a convenience that not many people have asked for; it obviously has more storage capacity than the built-in RAM.
Problem with the built-in RAM is that of the battery ever runs flat, it will loose its content. So it's your call if you need permanent storage next to e.g. the EEPROM storage in an AVR chip (e.g. 328P in an Uno).