Is it secure?

[Bootsock]

P2P isn't secure unless it's encrypted, but that doesn't seem to be the case for ED. You can go in to it's log files and find peoples IPs and even machine names. Not good :/

A slightly incorrect assumption. Even if the connection was encrypted, looking at the traffic would still disclose the point to point IP addresses as it would only be the payload which is encrypted. Also, as the connection would need to be decrypted on the client machine you could still get to information stored in memory in cleartext.

Does anyone know if using a SSL Proxy would enhance the security? (A paid for private proxy, not a public one).

Not really, because if there's any vulnerabilities within the code which were exploitable then the proxy would just pass them onto you.

It might make you feel better, but at the expense of increased latency.

So I still don't know if I should be concerned about security when playing this game.

The question is, how much do you trust the code and the developer? All code will have exploits, it's just that they may or may not have been found yet. Your PC name, IP address and much more will be available in other places already, it's just you probably don't know.