Accepting a social login compared to traditional login

Can the username be omitted if there is a profile picture for an Account Options button?

It could be instructive to see how other big players deal with it. If the "big guys" do, it is reasonable to assume that many of your users will be familiar with the approach. Here is a non-scientifically picked example based on what I just opened in Chrome at the moment ...).

Facebook

Avatar | Surname

Twitter

Avatar only

Stack Exchange

Avatar only [but with badge as part of the same link]

Quora

Avatar | Surname

JIRA

Avatar | Down arrow

Zendesk

Avatar | Down arrow

GitHub

Avatar | Down arrow


So I would say that D. should be out - nobody uses this style and, as mentioned elsewhere, the link 'Name' merges into the menu items.

I would B. to prefer. It's pretty widespread (but note that Zendesk, JIRA, and GitHub tend to attract more power user types). I also think an arrow is more affordable than the name link. If you choose the avatar and name combo I will make sure that both are connected (i.e. hovering over one of them will highlight both items). Check out how Facebook, Quora, and Stack Exchange handle it.

In short: Yes, the username can be omitted.