I am a beginner, would like to know if I can start a short story calling my main character "he" and then introduce his name later. If so when is a good time to do this?
Yes, you can do it, but it presents added challenges for she story telling. It is even possible to have a character never be introduced.
Now, for the hard questions: Should you do this? When should you introduce a character? The answer to these questions is the same, and deceptively simple: It depends on what fits best with the story you are telling.
Thats why editing your own story is important.
In first draft, just introduce the character when you feel it is important. In second draft, however, do re-read your story and decide when the point is right.
And in third draft, decide on the actual name of the character.
Recently, I finished On Writing by Stephen King and since then, I do follow this advice.
When he wrote The Green Mile, the name of main character was changed in late stages, when he decided on significance of the name.
Yes. You can very easily start a story without naming your character. An example off the top of my head would be the Hunger Games. The name of the main character isn't introduced until page 5, if memory serves. However, that novel is written in the first person.
If you are writing in the second person, you will need a bit more than simply 'he.' You will need some sort of title, something to associate 'he' with. 'The man' would work just fine. As eladrin201 mentioned, this could be a good place for description (though I would suggest you show that he is tall rather than say it. 'His head bumped against the chandelier.')
Now when is a good time to introduce your character's name? Soon. The reader wants to know the name, and if you keep that info from him for an extended amount of time, he will get frustrated and start looking for reasons to leave. Introduce the name within the first chapter for sure.
In my experience, a name needs to be revealed once there is interaction with another character. At that point, you can't rely on pronouns, or your reader might get mixed up. In The Hunger Games Katniss's name is only revealed once Gale enters the stage and starts talking to her. Previously, there was no real need for us to know her name (and no really good place to inform us without it seeming unnatural).
One last thing about pronouns: be sure it is clear who they are referring to. Even if there is no interaction, constant uses of 'he' or 'she' can get redundant. The reader will start to pick them out in the same way he would a word that is used too often. Be sure to intersperse your pronouns with other words: 'the man,' 'the figure,' 'the sleuth,' etc. In my experience, you will need to use a title like this once every 1-2 paragraphs, more or less depending on what you write (Be sure to not use the same one every time). Just be aware of how things are sounding.
Yes. Don't put your character's name in until it feels necessary. Someone calling your character's name can be much more impactful than the narrator saying it, and the way that it's said can also inform the reader of their relationship.
Names aren't always necessary, but they help the reader to picture the character in their head. If you want to maintain a distance between the reader and the character, don't name them, or call them 'Mr/Ms Jackson'.
The longer the piece, the more difficult it is to get away with not naming your character. However, there's nothing to say that you can't refer to him as 'he' in the first draft and change it later on, once the idea is down.