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Sounds like you are trying to forward your site, not transfer it. Check out this article that will explain domain forwarding here. Forwarding with masking is when the URL you are forwarding your domain to is not displayed in the browser, just the domain. Forwarding only, is when the URL the domain is being forwarded to is displayed in the browser bar.
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If you have registered a domain with GoDaddy that you want to have directed to the website that was provided to you by the new company, you can FORWARD the domain. These instructions will help.
If you have created your own website with GoDaddy, but want those with the company address (URL) to get directed to the site you made here, it's not likely that you have control over their assigned URL (https://www.thatcompaniesname/yourname). You will need to either contact them for instruction, or create a link on their home page that your visitors can use to get to your GoDaddy website after they arrive there.