That's a good question. It is difficult to say. Some people like to have their name abbreviated, some don't mind, and some hate it. Some people don't mind if friends do it, but think that it's rude for workmates to do so. In general - listen to what others around call them. If you are not sure - ask them if it is OK. I don't think there are any fixed rules, and there are certainly some odd ones. And those vary somewhat with country too. David -> Dave, Daniel -> Dan, Peter -> Pete and Robert -> Rob or Bob are quite common. Barry can be abbreviated to Baz, or even Bazza used to be common in Australia particularly.

Do you mean like this? Someone's name is Viktor and you call them "Vik"? This is called a nickname, if you are friends with someone you can make up your own nickname for them, of course! Some people are always called by their nickname (by friends/family), then it might be okay to call them by their nickname. But generally speaking it's for friends.

What do you mean by abbreviations? For example Mr. Mrs. Ms (miss)

The rule for abbreviation of names is "follow the person's lead." Use whatever form of name the person himself used the last time he spoke or wrote to you. If his letter ends "Very sincerely yours, William F. Endicott," begin your next letter, "Dear Mr. William F. Endicott." If you meet him in person, and you need to speak first, begin "Mr. Endicott..." and he will probably say, immediately, "Willam." Or "Call me Bill." Err on the side of formality and let the person you're speaking too correct you. If the first meeting involves a friend introducing the two of you, "Danny, this is Billy," then you can use the name in the form the friend used it.

What do you mean abbreviate? Do you mean adding Mr. Mrs. Miss (Ms.)?