How to identify a whole house water filter type?
It looks like a standard whole house filter similar to this one. Replacement filters can be obtained at almost large hardware, orange or blue store.  There is a variety of Replacement filters that are for sediment, charcoal for taste, and others. I use a similar filter at the kitchen sink to remove the chlorine taste of the city supplied water. You could shut off the water, remove the filter and then reinstall the reservoir part, and take the removed filter to the store for a replacement.