The factory charger / converter on a modern RV will fully charge them and do a great job of not overcharging them.
It was units built before about 1990 that had 'Converters' that are not voltage regulated, and on low voltage input will barely charge the battery. To avoid overcharging they have two circuits, one about 40 amps to run the lights while on shore power, and the other transformer is only 5 amps, just to charge the battery a little while on shore power to avoid overcharging it if the voltage is to high. But they have not been installing this sort of converter in RV's since reliable electronic ones came out in 1989.
Your unit should have come with a 45+ amp converter/charger that is a silver box, and has heavy duty wires running to the battery or 12 volt DC distribution box. It will charge your battery in about 4 hours to 90% full, and fully charge it in around 12 hours, and let it sit between 13.1 and 13.4 volts, regardless of the input voltage (between 95 and 130 volts).
Just check the water level once a month or so, until you get an idea of how often you need to add water. If you need to add water to frequently, then the voltage might be a little to high. But if you need to add 1-2 quarts every three months, it is about average.
Most portable chargers can only put out around 15 or 20 amps. The one listed above is rated at 40 amps full time, and probably cost well over $100. You can get one if you like, but it will be rarely used unless you do a not of dry camping, and don't buy a $200 solar panel rated at 140 watts, to charge it in silence. Solar has become a lot less expensive than in years past. My 120 watt panels cost $429 back in 1999, much less per watt than my pair of 45 watt panels for $750 back in 1994. You could rent a nice sized house for $750 a month back in 94.
Of course only used distilled water in the battery.
Good luck,
Fred.