SQL Licensing on Azure, Standard D4 Windows 2012 Server 8 core, is it 1 phsysical core?
At the risk of stating the obvious, nothing is physical in Azure as far as you are concerned.  The best thing you can do is go to the Azure Pricing Calculator, find the 'SQL Server' section, select the 'Standard' section, find D-Series, select 'D4' and slide the slider to 1.  That's what you will be paying, eg



SQL Server will treat that box as having 8 cores, so should you.  You can also compare and contrast costs, eg try Enterprise edition.  As far as running coreinfo on Azure goes, don't bother unless you've got some time to kill.  By signing up to IaaS you have resolved to care much less about that kind of thing, freeing you up to concentrate on the software.

If you are concerned about performance you should cast your eye over this superb article:

Performance Guidance for SQL Server in Azure Virtual Machines
https://msdn.microsoft.com/en-us/library/azure/dn248436.aspx