Assuming you have "Obtain an IP address automaticly" enabled in both circumstances: wired and wireless, and hence, not a static IP, the issue is one of tcp/ip property differences, and name resolution issues.
1. Make certain under the Advanced button, WINS tab, that you have "Enable Netbios over TCP/IP" checked for both your wired and wireless connections; that Netbios is the default protocal in both settings; that no other protocal is used in either setting (IPX or Netbui); and that without error you can do an Ipconfig /release, Ipconfig /renew sequence from the worksation.
If any of the above is not exactly right, your issue is a likely result.
2. If you find yourself going back and forth with a logon to a Workgroup with Netbios as the name resolution under Windows, you really should consider using Netbui for all clients, XP or pre-XP. Or disabling the "Computer Browser" service under this laptop. Or both.
I suspect you are confounding name resolution through traditional Browser services with all this testing.
If it is a test of Netbt, then make it a fair test by specifying the Master Browser, secondary Backup Browsers, and disabling the ability of clients to assert their own notion of being Master.
If this is a regular, and practical matter, disable Computer Browser service on the laptop, and possibly implement Netbui Workgroup-wide to simplify matters.
Forum member Bob Lin has written extensively on this issue, and I recommend strongly you look at his Troubleshooting site under "Browser Issues":