My ebike battery totally died today. I can't find the model number for the battery as it is not written anywhere.
Here are the pictures:
That battery case is a common form factor, often called "ebike battery case 03". Based on labels, your battery has 36 V voltage and Li-ion chemistry.
Same case type batteries are still sold in many places online. It doesn't have to be same brand as the same case design is used by many battery pack manufacturers. The voltage should be kept the same, fortunately 36 V is the most common voltage in this case size.
Generally if you keep the same battery chemistry (Li-ion) and do not switch to e.g. LiFePO4, you can use your old charger. But if you are unsure or there is a difference in chemistry, buy a new matching charger for the new battery pack.
Its a ZAP brand bike, with their custom battery pack. You'll need to buy one of theirs either directly or from a reseller.
Strangely, https://www.zapebikes.com/products.html does not list replacement batteries as something you can order.
With some technical know-how it may be possible to replace the cells inside the battery, but that's more of a question for for electronics.SE
If you can't get a new battery, you might be able to get a company to rebuild that battery pack with new cells. I've had good luck with these people:
They were very responsive and were willing to put in a specific charging port for me. I've also heard batteriesplus will do similar things.