Unable to authenicate after IP changed into URL

Question

Hi there, 
We have Sharepoint 2013, and it has 2nic card, one public and one private IP. 
The private IP is used to talked  to the DC that's in the same private lan. 
We were able to authenticate and get into the sharepoint perfectly fine when it was  IP based, as soon as we changed in into the URL, and access it via URL, it is not taking our authentication at all.  
I feel like it is trying to do authentication from outside to inside, because I don't even see the log on my DC at all. 
Why is this happening by changing from IP based to URL...
Thanks! 

Answer 1

Figured it out.   Thanks tho!  
Apply the following registry change to the file server to which you installed the hotfix. To do so:
Start Registry Editor (Regedt32.exe).
Locate and click the following key in the registry:
HKEY_LOCAL_MACHINE\System\CurrentControlSet\Services\LanmanServer\Parameters
On the Edit menu, click Add
Value, and then add the following registry value:
Value name: DisableStrictNameChecking
Data type: REG_DWORD
Radix: Decimal
Value: 1
and then you can create a registry key, back connection host namehttp://support.microsoft.com/kb/896861
Click Start, click Run,
type regedit, and then click OK.
In Registry Editor, locate and then click the following registry key:
HKEY_LOCAL_MACHINE\SYSTEM\CurrentControlSet\Control\Lsa\MSV1_0
Right-click MSV1_0, point to New,
and then click Multi-String Value.
Type BackConnectionHostNames, and then press ENTER.
Right-click BackConnectionHostNames, and then
click Modify.
In the Value data box, type the host name
or the host names for the sites that are on the local computer, and then click OK.
Quit Registry Editor, and then restart the IISAdmin service.