Doing it directly in the car doesn't make much sense. You need a big battery to power the electrolysis that generates the hydrogen. But if you have a big battery, you might as well use an electric motor and have an electric car.
Doing it indirectly, using mains electricity to make hydrogen, then using the hydrogen to power a vehicle, is possible and lots of people have tried it. But it's never caught on. It's less efficient than a battery vehicle, and we don't have the infrastructure in place to transport the hydrogen.
In anything more than small volumes in either very strong, ( or expendable) containers you must keep the H2 and O2 separate until you want them to burn. Given we have O2 in the atmosphere, it is easier to vent the oxygen and just carry the hydrogen, but as it does not liquefy at any sensible combination of pressures and temperature, storage requires high pressures, and is a pain.
