It looks as though ymail is just the same. I'd not heard of it, but it sounds like they just got a new domain so they could say "you can have that name you always wanted"
If you want to pick your own domain name then as said you need to check if it's available. it might be available as yourname.net, yourname.com etc
If it is you have to pay a small yearly fee to register the domain name AND a fee to a hosting company for the mail to go to. They provide the actual disk space for your mail to sit on before you read it.
You can get just email hosting or webhosting that includes eamils.
I can get web hosting and email hosting and the domain name thrown in for $4 a month from arvixe.com. Many people recommend 1-2-3 Email Hosting though I've not used them
I prefer having my own domain name because you don't just get one email. You can have firstname.lastname@example.org, email@example.com, etc etc