I am writing about my life experiences and I want to use email correspondence between myself and another to tell part of the story. I have not used real names in my work and have altered the emails accordingly. Do I need permission to use these emails?
I guess the answer will depend on your country. In many European countries, emails fall under the "Secrecy of Correspondence", and breaking this can result in a prison sentence. What the laws of your country say about this, I wouldn't know. The Wikipedia article mentions the situation in the United States.
Another legal question in this situation is reputational damage. There may be more, so I would ask a lawyer.
Finally, you might want to consider if your relationship to the sender of the emails or his family and friends will suffer and if you want that – and how you generally feel about breaking another person's confidentiality. I wouldn't like it, if someone published my emails to them, so I wouldn't do it unless I felt the general public needs to be informed of some illegality.
For what you need to do legally, you'll need to consult a lawyer in your jurisdiction. Laws vary. The rest of this answer is about practical considerations.
First, are you on good terms with the person whose email you want to use? Do you want to be on good terms after you publish your work? If so, then talk with this person. Nobody likes surprises, and there is a presumption that private correspondence is, well, private. (If the email came from a large, well-distributed, archived mailing list, that's a little different -- but I would still ask.)
Second, even if you change the names, given a large-enough corpus a person who knows what he's doing can identify the person (to a fair degree of confidence) anyway. Everybody writes with certain "markers" that help to identify their work; what they are varies and you probably don't know you're doing it, but you are. This isn't just spy-agency stuff here; corpus analysis is a standard tool in fields like linguistics and statistics -- and, for that matter, certain software domains. What this means is that scrubbing the names doesn't necessarily anonymize.
I recommend that you first talk with the person about your desires, and then work together with that person to transform the email you want to quote in a way that satisfies both of you. This could involve selective quoting, summarizing rather than directly quoting, and/or rewriting passages (that is, you do the rewriting, not the original author).
IANAL, but I think if you don't reveal the identity of the other person and there's nothing that can help other to relate him with your story, it is not a problem.
But, just in case, I will ask a lawyer or, better, the other person if you can use those mails. If it's for a good reason, I think the other would help you.