Unless DynDNS has changed their policy recently, I think they switched to a for pay Dynamic DNS addresses, a few years ago.
I've been using NoIP.com free dynamic DNS names. I have to confirm I'm not a robot once a month, but otherwise they work fine.
Big note. If you open your ftp server to the internet, you had better have some very strong passwords, as port 21 is well known and bound to have script kiddies pounding on it. And you do NOT want to allow anonymous access, otherwise the same script kiddies will start chewing up your up-link bandwidth.
You might be smarter to use it as an sftp server (ssh's version of ftp) as it is more secure, passwords are not going over the net in clear text, you can use ssh-keygen keys for easier access from frequently used computers, you can easily use a different ssh port number instead of port 22 (another well known port). For example:
sftp -P 55522 username@dynamic.dns.name
While this is security through obscurity (which is not really security), it does cut down on well known port attacks. You still need good password protection.
Also ssh allows for the use of 'scp' which is more versatile, especially in a shell script situation (or even Applescript).
There are GUI based ftp clients that also work with sftp on both Mac and Windows (for all I know Linux as well).
You enable ssh via System Preferences -> Remote Access (again, if port forwarding to the internet, make sure all accounts on your system have good passwords).