Looking for help identifying/fixing a bike
Fortunately, bicycle chains are standardized. You do not need to know the model of the bike in order to buy a chain for it.
There are two types of chains: narrow derailleur chains and wide non-derailleur (single speed) chains. Your bike does not seem to have a derailleur, so it is probably using a wide non-derailleur chain.
The non-derailleur chains are 1/2&quot; x 1/8&quot; in size. You also need another spec, i.e. how many links there are in the chain. You can count them in the old chain.
However, if the chain keeps popping off, you don't necessarily need a new chain. You may need to adjust the chain tension. Looking at the bike, I don't know how easy it is to adjust the chain tension if it is at all possible. Most good single speed / hub geared bikes have horizontal dropouts, allowing you to loosen the wheel, move it back, and tighten it to get more chain tension.
If there's no way to increase chain tension, then you need a new chain. In any case, a new chain might be a good idea even on single speed bikes even though they are not as likely to cause expensive damage to rear sprocket with an elongated worn-out chain.