If you only make use of the yola subdomain eg. *mysite.yolasite.com*, then it will be yours for as long as you are with Yola. If you had to close your account you would then forfeit that site name.
However, if you purchased a custom domain through Yola eg. *mysite.com*, it would remain yours regardless of where your site was hosted.
We have a tutorial that contains the steps to purchasing a domain from Yola: Buying your own domain from Yola.
When you choose to buy your domain from us, you can pay with a credit card or PayPal. If you don't have access to a credit card, you can credit your PayPal account by transferring money from your bank account to your PayPal account, see this link for more information.