Generally vSphere doesn't deal with IP, only ethernet - but there's two exceptions to this; if you're using NSX and if you've configured a 'Network Protocol Profile'.
Firstly just ask you VMware people if they use NSX, if they do then they'll have a lot of control of how DHCP works and can help you based on their designs.
If they don't have NSX then it could well be one of these 'Network Protocol Profiles' - this is a v7 name (it used to have a different name in previous versions but I've forgotten its name sorry) anyway it's set at the 'Datacenter' level, if you have appropriate permissions you could select the datacenter that contains thew cluster/host that manages your VM, then under 'Configure' you should see 'Network Protocol Profiles' - if one or more are in there then you can find the one that applies to your VM (they're usually assigned to port-groups or networks) and see how it's setup.
If you have none of these then I suspect you have an external/non-VMware-provided DHCP service running, again your server/networking people should be able to help.