Fish can learn to recognise people, yes.
They don't need to learn to recognise faces, there are many factors that make people different; such as build/size/the movements you make. Things you might not even notice but your fish/other pets will do.
Fish are actually pretty smart animals and they do actually have good memories. Some can be taught tricks. They also learn that food comes in at the top of the tank and many will recognise when they are being fed, you can even teach your fish that if you tap the glass they will be getting fed (although this can also scare some fish).
My fish has learnt that the first thing I do in the morning when I get out of bed is feed them, they know approx what time I get up, so my
Betta usually wakes up before me and watches me sleeping until I feed her. lol.
Depends on the species how well they can see, but most fish can see better when things are close up and less when they are further away. Some fish can see colours and lights better than others, depending on the species. For example; deep sea fish don't have good vision because they don't need to see in the dark.
Although fish (most) do not have the ability to hear, instead they have an sense organ called a lateral line, it runs along the side of every fish and it detects the vibrations in the water, so they probably will not recognise voices as they can't hear them....unless you scream at your fish tank lol.
Sounds like your fish recognises the people in your household and know who feeds them. Xp