There are several ways to find the service tag of a Dell ESXi host. This post could be helpful to find the Service Tag of a Dell ESXi Host remotely. You need to establish either a ssh or a console session to the ESXi host.
Type in the below commands:
[root@localhost:`] cd /bin
[root@localhost:/bin] cd /sbin
[root@localhost:/bin] esxcli hardware platform get
You should be able to find the service tag under Serial number.