I'm unable to access the SharePoint Url with the site name
http://hhhhhhhhh/sites/example, but when I use the IP address like this
http://10.44.38.43/sites/rover - I'm can get into the page.
Can anyone help?
You should check in SharePoint (if 2013) Central Administration -> System Settings -> Farm Management -> Configure alternate access mappings if you have added your server address: http://hhhhhhhhh
If not, you should add it. Here you can see how it should look: http://www.ivchenko.pro/SiteAssets/Lists/Posts/AllPosts/alternate-access-mappings.png
Hope it helps.
Login to SharePoint server, check if the site is browsing with site name i.e http://hhhhhhhhh/sites/example on the server (you may have to add a host entry for hhhhhhhhhh in your host file.).
If the site is browsing fine there, then its most probably a DNS level issue not the SharePoint one. Apparently it looks like your DNS is not resolving the web address and when you type the IP manually, it works.