Can't access the client PC using that Computer Name

Clarifications

Also ensure you have netbois enabled, check the DNS server could be a problem with it, make sure the IP repersents the Name of the machine.

This behavior can occur if both of the following conditions are true:
1. NetBIOS over TCP/IP is not turned on (enabled) on one or more computers in the workgroup
2. The Computer Browser service is not started or is turned off (disabled) on one or more computers in the workgroup.

Try following these steps to see if fixes the problem.

Step 1: Turn On NetBIOS over TCP/IP
1. Click Start, click Control Panel, and then click Network and Internet Connections.
2. Click Network Connections.
3. Right-click Local Area Connection, and then click Properties.
4. Click Internet Protocol (TCP/IP), and then click Properties.
5. Click the General tab, and then click Advanced.
6. Click the WINS tab.
7. Under NetBIOS setting, click Enable NetBIOS over TCP/IP, and then click OK two times.
8. Click Close to close the Local Area Connection Properties dialog box.
9. Close the Network Connections window.

Step 2: Start the Computer Browser Service
1. Click Start, right-click My Computer, and then click Manage.
2. In the console tree, expand Services and Applications.
3. Click Services.
4. In the right details pane, verify that the Computer Browser service is started, right-click Computer Browser, and then click Start.
5. Close the Computer Management window.

Hope this helps

Do you have a DNS server?

Is this all on the same subnet, or is this PC on a separate local and/or remote subnet?