The computer's IP address will update on its next Discovery Data Collection cycle. You can force this to happen by running this command on the client:
WMIC /namespace:\\root\ccm path sms_client CALL TriggerSchedule "{00000000-0000-0000-0000-000000000003}" /NOINTERACTIVE
This is the list of all available actions:
Application Deployment Evaluation Cycle: {00000000-0000-0000-0000-000000000121}
Discovery Data Collection Cycle: {00000000-0000-0000-0000-000000000003}
Hardware Inventory Cycle: {00000000-0000-0000-0000-000000000001}
Machine Policy Retrieval and Evaluation Cycle: {00000000-0000-0000-0000-000000000021}
Software Inventory Cycle: {00000000-0000-0000-0000-000000000002}
Software Metering Usage Report Cycle: {00000000-0000-0000-0000-000000000031}
Software Updates Deployment Evaluation Cycle: {00000000-0000-0000-0000-000000000108}
Software Updates Scan Cycle: {00000000-0000-0000-0000-000000000113}
Windows Installer Source List Update Cycle: {00000000-0000-0000-0000-000000000032}