MOSS 2007 – Welcome name is not updated problem.

This is a very well know problem.  Even if you run full profile import on sharepoint 2007 the user’s which is name property has changed in AD , not updated on your site welcome name.
First of all you have to detect that the problem has encounter between Sharepoint and AD connection issues. If you see the updates in Profile Store in SSP correctly but not affecting welcome name this article may help you. If it is not updated correctly in Profile Store , it is another problem that out of scope for this article.

So what you can do :

Here is the command for force the sync operations.

stsadm -o sync -ignoreisactive 1
stsadm -o sync -deleteolddatabases 0
stsadm -o sync -synctiming m:5
stsadm -o sync -sweeptiming m:5
stsadm -o sync

Wait min 5 minutes. and check.

You can get more information about stsadm -o sync operations.
http://technet.microsoft.com/en-us/library/cc263196(office.12).aspx
If this is not solve your problem you can use fallowing tool for a workaround;
https://blog.bugrapostaci.com/2012/01/22/sharepoint-tools-wsscontentdbsync-v1-0-command-line-tool/