If I remember correctly, the BCM57810 is a CNA and you need to add a software FCoE adapter (in the same Storage Adapters view; Configuration -> Storage Adapters -> Add):
Once that's done, you should see it in the list of storage adapters.
Note that FCoE can require some additional configuration on the network side of things, as well.
This blog post provides more information on the subject: Setting up Software FCoE on vSphere 5 - blog.scottlowe.org - The weblog of an IT pro specializing in virtualization, net…