My friend has seen videos that shows what kind of tricks dogs can do. (There are no instructions in them) In some of the videos the dog gives a paw and it's named like "paw" and "other paw". Are those suitable names and how does Lotta know which paw is "paw" and which paw is "other paw"?
The dog will learn whatever cue you want her to. So your friend should pick out a cue she wants to use for the right paw and a cue she wants to use for the left paw. She make one "paw" and one "other paw", she can make one "shake", she could even make no voice cue at all and simply teach Lotta to give her left paw when your friend puts out her left hand and her right paw when she puts out her right hand.
Since my friend wants to teach Lotta to shake with both paws and she first teaches one side, should she name the behavior when she has teached one side? If so, how does she know when should she name it?
Teaching two paws might be a little tricky because you want to make sure you don't discourage her from using her second paw while you are teaching her to use her first paw. So if you are teaching her to shake with her right paw first you want to make sure you don't accidentally stop her from wanting to ever use her left paw. I've never taught a dog to use both paws so I'm only guessing.
I would probably teach them both at the same time using different hands. First I'd encourage Lotta to paw at your hands with either paw. To do this you can wiggle your hand around on the floor or playfully tease her so that she paws at your hand, then reward her. Repeat this until she is quickly, repeatedly pawing your hand. She can use either paw/both paws, you just want her to learn that you want her putting her paw on your hand. So get her to be good at this using both of her paws.
Once she is good at pawing you can start teaching her to use a certain paw when you hold out a certain hand. So if you want to start with her right paw you would hold out your right hand. If she paws with her left paw just ignore her and keep your hand there. When she uses her right paw then you can reward her. Do this several times until she seems to get it. Then do your left hand and wait for her to use her left paw. Again wait until she does it correctly several times in row. Then try the right again. Then the left again. By doing only a few repetitions of each hopefully she will not stop using the other paw.
Once she has learned to use her right paw when you use your right hand and her left paw when you use your left hand you can add in voice commands before you offer the hand. So for example you can say "paw" then offer your right hand. Then say "shake" before offering your left hand. This way she will learn the different verbal cues for the different paws.
Some of the tricks are teached by targetting. When you teach the dog to target hand and a Post-It, do you name both of them touch? If you later teach the dog to target a Post-It also with his paw, should you name it differently?
When I have a dog target my hand or another object with his nose they both have the same name. If I want him to target something with his paw it would have a different name than when he uses his nose. For example using his nose I would say "touch" and using his paw I'd say "target".