editing /private/etc/hosts
/etc/hosts can't be used for that:

/etc/hosts cannot be used (by itself) to produce hostname &quot;aliases&quot;.
The hosts file produces the internal equivalent of A and PTR records from the DNS, i.e. mapping of hostname to IP address and vice-versa.
It cannot be used to produce the same effect as a CNAME record.

You can make ssh alias equivalent to ssh host.no-ip.biz or ssh username@host.no-ip.biz by adding lines like this to ~/.ssh/config:
Host alias
HostName host.no-ip.biz
# User username