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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 m...
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#3: Attribution notice added
Source: https://writers.stackexchange.com/a/16027 License name: CC BY-SA 3.0 License URL: https://creativecommons.org/licenses/by-sa/3.0/
#2: Initial revision
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.