How to pronounce @[name] on Twitter?

Technically, @ is always pronounced as at because that is what it stands for. Nevertheless, @John can mean different things in different contexts, such as contact John. Read it the way you would be best understood.

I think the @ symbol may originally have been used for this exact purpose, actually. To my knowledge it was originally used in e-mail, where the writer was supposed to think of a person as being 'at' a particular place; so, when writing the e-mail as To [email protected], the writer could be thinking they were writing to John at Berkeley educational institute.

With Twitter (and other systems which prefix usernames with @), the meaning changes a little, in that the @ is no longer prefixing the person's location, but the person themselves. However, when addressing a message to a person, it could conceptually be substituted with the word 'at' and still make sense.

I'm tweeting the message at John216.

So in the above sentence, 'at' is performing a double task of both being a preposition, and indicating that the @ character begins the person's username. Of course in English, you'd generally use 'to' instead of 'at' there, but language evolves. In addition, the word 'at' may be convenient to indicate that there is a subtle difference between tweeting 'at' someone and saying something 'to' someone; with a tweet, you're kind of doing a "fire and forget"; you don't know whether the person will read the message, but you're addressing it to them. If you say something 'to' someone, you know they're hearing the message.

Maybe sending online messages 'at' usernames will become a new common expression?

"@Tom" just means "Twitter account Tom"

If you want to say contact Tom, you should write something like:

Tweet @Tom for more information - the @ is always pronounced 'at'