Well, instead of starting off with the races, I like to do a bit of worldbuilding myself, and on a scientific standpoint, creating the races off what I believe would be best suited and well adapted for that particular habitat. For example, if we were going with a world with very diverse terrain samples, such as deserts, rainforests, volcanoes, caves, mountains, grasslands, oceans, and tundras, it is possible that years of isolation could change species and form several subspecies with different evolutionary adaptations.
For example, let us say, elves. Not the traditional elves, so we can call them not-elves. Elves are said to mostly live in woodlands, so we can work with that, for starters. These not-elves could come from heavily forested regions where little light and little of value reaches the forest floor, so they have remained arboreal, like our simian ancestors. Consequently they are light, deft in movement and have excellent spacial awareness. If you wanted to break from the classic fantasy norm, you could make them animalistic, with long arms and fingers, strong for climbing and swinging between branches. Elves are normally portrayed as a refined, noble folk, so making these not-elves savage and into tribal hunter-gatherer tribes is a good twist in my opinion.
As for dwarves, we can call this equivalent, not-dwarves. Dwarves are usually either said to live underground or mountain caves. Either way, a smaller body and shorter limbs are strongly selected for as it allows them to travel deeper and escape through narrow crevices, escaping dangers of various kinds such as predators. To break from classic forms you could give these not-dwarves some of the adaptations of cave creatures - lack of skin pigmentation and melanin, poor eyesight, rough skin.
As for a race inspired by the Giants, we can call them not-giants. Giants usually live in the arctic and high in the mountains, they would likely have lots of hair, fur even - if you want to make an anthropomorphic race - to stave off the cold. They would also be adapted for lower oxygen conditions, meaning a larger chest volume and lung capacity, so larger torsos and taller people.
As for mermen/mermaids, we can call these not-mermen for now. A race that lives in swamps or aquatic bodies would likely have gills, webbed hands and feet. They would also, much like other smart aquatic mammals like dolphins, would use echolocation to communicate. Dolphins can produce clicks with their vocal cords; your humanoid should be able produce a similar sound. If not, some slight change of their vocal cords should make it possible. Blind humans have trained themselves in echolocation as well. However, the human brain is not set up to be used this way and can't do as effectively as a dolphin. Dolphin brain is optimized for interpreting sound into sight. Your humanoids would probably have a brain that was a hybrid between a human brain and dolphins.
I can't think up of names, but here are some ideas for races.