Changing URL

I am rebranding and need to change my current URL (and WP account if possible). Currently I am monogramsandmakeovers.com and would like to change to yellowdogpress.com. I have purchased the new domain through Go Daddy and have hosting with monogramsandmakeovers.com with Go Daddy as well.
How can I change to my new URL but still keep my current content?
If someone visits the old URL will it automatically take them to the new URL?
Will I keep my current WP account or can I set one up under Yellow Dog Press and still keep all my content/information/theme, etc?
Will my hosting have to change as well to use the new URL?

Thanks for your help with all my questions!