There are 2 ways:
1. Open putty and run any of below commands and see what you need:
esxcfg-scsidevs -l
esxcfg-scsidevs -l | egrep -i 'display name'
2. Open web client connection directly to ESXi host. Select "Storage" under Navigator panel. ESXi will then open "Datastores" panel on right. Open Devices tab. The serial number should be located at the end, after the device's model number.