How can I introduce myself when I text to someone who knows me for the first time after I got her number or when I use a different phone number or when I send an email?
Usually, I use "I am (Igor)."
Is it correct? How is the difference from "this is"?
I suppose just of "feeling" (AmE and BrE).
This is X (or just It's X) are more natural when introducing yourself to someone who knows you, but doesn't know you're the one speaking or texting.
I am X or My name is X are - in my opinion - better used when introducing yourself to someone who doesn't know you, or doesn't know your name.
A good way to remember that is to consider which question you've been asked - an English speaker would typically ask *Who's that?*or Who's speaking? in the former case, and Who are you? in the latter.
In English you use the pronoun "it" until you identify the gender of the other person. For example: if you're receiving a call and you don't know the number, you should ask: "who is it?" and the person who's calling should answer: "It's (Mary)". In other case, if you're calling someone you should introduce yourself like: "This is/ It's (Igor)".
