Almost certainly not. I've had hundreds of email accounts and none of them have required me to provide my (real) name. (Or, if they have, I've simply entered a false one anyway)
If the domain name (= the bit after the @ sign) is an email provider that anyone can use (e.g. gmail.com), then even that provider probably doesn't know the real name of the account holder.
If the domain name is that of an ISP (e.g. orange.co.uk) then the ISP will know the name of the person who registered that address, but (unless you work for the police or security services, and have a genuine need to know) they won't tell you.
If the domain name was actually registered by the person sending the email, then a search of the Nominet 'Whois' service (for addresses ending in 'uk' only) will show who owns that domain name:
http://www.nominet.org.uk/other/whois/
(However a non-trading individual can opt to keep their details hidden).
For non-UK domain names you might find the details here:
http://www.whois.net/
Chris