This will begin with a little reference to my background to justify my conclusions at the end. I started rebuilding my alternator a long time ago after struggling for for several years plus multiple attempts to fix a battery using excessive water problem. Replaced an OEM alternator with a rebuilt alternator from a major auto parts store, same problem, new battery, same problem. Finally had a well respected automotive electrical shop test the system and its voltage regulator. They saw no trouble but reluctantly did reduce the voltage output to its lower limit. Can't do that today. Better but still using water
My replacement alternator's front bearing started to fail some years later. I decided to rebuild it myself. Reading my factory shop manual one line at the time, testing everything, found one bad diode out of 6 diodes. Replaced the bearing and one diode, no more excessive battery water usage. How could a person be so unlucky to have a alternator fail and then buy a factory rebuilt alternator with the same single failed diode problem? After that I have always rebuilt my own alternators and starters. I also in the past visited one shop that rebuilt alternator, they were nice people. I was looking for some spare replacement diodes and they graciously sold me some from their working supply of used core parts. I saw no new diodes there. I have also noticed that many rebuilt alternators came remarked all with the same amperage output. Maybe not a problem unless you have a high output alternator or a later year improved model. I had a neighbor later that owned an auto parts store and I had access to his parts catalogs and store. I had later found a good source for new replacements electrical parts but they have now retired and closed their shop.
So my suggestion if your going to purchase a rebuilt alternator keep your old OEM core, for sure until your really sure its an exact replacement and it's working well. This becomes especially true it there is anything special about your electrical equipment such as higher amperage alternator, maybe a starter that possibly came with a heavy duty option. My observation is re-builders like to make one unit replace everything and the parts house enjoy their benefit of stocking just one part number. After all who will ever know? If you have your OEM unit sill in your hand, you have a good example and path back to an easier recovery.
One thing I can tell you if your alternator has an adjustable belt tension buy a belt tension gauge. My failed front bearing failure ended a long time ago after buying a belt tension gauge. About 1/4 - 3/8 inch to my suprize at the time can change a belt tension from too lose to too tight.
Good Luck, may everyone's alternator and starter last forever.