Is there an email service like Gmail but not overloaded by nicknames? I need a good IMAP service with quite good capacity of storage. By the way, I would like an account name like name.surname@..
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You can register a new domain and use Google Apps for free. Google Apps includes a fully-featured Gmail, as well calendar and several other Google services.
You'll be able to register accounts like
For example, I registered a domain with my family name and I'm providing email accounts to all my family
The only cost will be the yearly domain registration cost. A .com or .net domain costs between $5 and $15 per year, other extensions might have a different price.