Is it possible to change your domain name? Is there a certain amount of time that you would have to wait to do so? I bought allofthekingshorses.com 1/2 year ago and now find that I need a different name for my site. I would just purchase a second domain, but I don't need the first one anymore.

if you are looking for refunds than, there is no such thing as refunds when you buy any domain name. I would suggest putting that domain for an auction, do a google search on the net for domain auction and you bound to get lots of hits.

or if you want to change your main domain name for your hosting account you need to open a trouble ticket and explain to them.

I know there is no refund on domain names. The domain name I have is the one that I got for free with my account, which is why I was wondering if I could change it and if so, if I had to wait a certain amount of time. When hostony registers you domain, do they do it for one year, two years, etc.? And whatever time they register for, instead of just renewing it, can you get a different one? That is what I am wanting to do.

Please contact billing@hostony.com.

which is why I was wondering if I could change it and if so, if I had to wait a certain amount of time.

Sort of depends on what you mean by 'changing it.'
Some hosting plans like the 'Special' plan let you have multiple domains ... so then it'd be a question just adding that domain and letting support for the other one lapse.

I can't say this with any authority, but with the 'profi' plan you'd prolly have to pay some sort of fee to change primary domain, but it's not in their interest to keep you 'locked' into that domain. It's more money for them and a happier customer if they can just charge you a fee to switch primary domains. At worst you could pay $3.95 a month for an 'addon domain'

Special plan allow you to add 10 full domains in your Control Panel and have one free domain. It means that if you want your other 9 domains to work you should also register them.