In professional, written correspondence (letters, emails), I would not mention my name ("Ich bin...") in the text at all.
I generally would consider this an Americanism (even in the UK I do not hear this very frequently). It has a rather unpleasant ring to it, and mainly reminds me of a bad sales pitch where some one tries to suck up to you. Also, it does sound a bit rude and patronising, as if the author does expect me to not know fully well what their name is - this is usually obvious from the letter head, signature or email footer.
(If you have none of these, you might want to revisit how you write professional correspondence. ;) )
As for how you know the person, this is a very different thing. If this is what you want to convey, my way of starting the letter is what @O.R.Mapper and @ Marakai suggested: in a matter-of-fact way. Describe how you know each other, mention what you have talked about, what you have experienced together, and so on - there is no need for mentioning their name:
Wir haben uns letzte Woche auf der Messe für Medizintechnik in Köln getroffen und ich hätte noch einige Fragen bezüglich ihres Produktes.
The only exception I can come up with in written form is that one might start with something along the lines of
Ich bin's, Gerhard. Lange nichts von dir gehört!
This is pretty much taken directly from how you might talk to a friend. This only works, if you are on a "Du"-basis with the other person, and even then only if you know them rather well. Even though the lines between "Du" and "Sie" are a bit more blurry nowadays, and it might be okay in your field to address people you have just met by "Du": If you have a need to introduce yourself, you are not close enough to use this.
I would never, ever use
Ich heiße Gerhard.
as this assumes that you actually do not know the other person very well.
Things are rather different of course, when it comes to spoken language, e.g. phone calls or meeting some one at a conference. Here, one has no way of knowing what the other person's name is.
You could introduce yourself e.g. with
Mein Name ist Gerhard LastName.
Gerhard LastName. (rather neutral)
Ich bin Gerhard. (less formal, I would not use it with a last name)
All of those are normally accompanied by a firm handshake ;)