You definitely don't need your photo on your SE profile to "prove" that it is yours. I don't have a photo on mine, yet everyone knows it's mine. If you don't use your real name, you can include your SE username in the same section where you list your twitter name, github account, code streamer handle, and any other online presence you think could help people know who you are.
I recommend you do this with a two-fold approach - one tiny speck of information for those who don't want to investigate further, and knowing that much more is there for those who want to check you out. So you might do this (with your info):
- Twitter @gregcons, 8000+ followers
- StackExchange Kate Gregory, silver tag badge in C++ on SO
... and so on. (You can include actual links to your profile, too.) This tiny summary of what you think is important may make an impact on a busy resume-screener, though it may not. It may lead some to check out your profile in more detail, to see what you're good at or what you care about. Rather than putting things in your profile to prove ownership, be prepared to answer questions about this activity: what is one of your best answers, and how did you come to know that? (The story you tell is a great way to describe yourself and your problem solving skills, good memory, industry connections, or whatever.) Which of these questions was the biggest relief to get an answer for? That sort of thing.