First I would say that having a big name surely help to start land a first job, however once you're in, you can definitely have a great career nonetheless.

I did not have a PhD and I don't know the US equivalent for what I have - Master - (I'm french), however even though I did some internship, I chose them poorly and it did not allow me to get relevant experience. Note to students: Don't choose your firsts internships poorly, you'll regret it.

So I started doing personal project and phone call started to ring after I put Nodejs and Angular in my resume even though I just did some useless shit with it, and wasn't ready at all for productive work. Luckily enough, a recruiter working for a startup pass me along a test that wasn't for me, and I did it better than the original dude so I got my first job.

TLDR: Use your expertise to make some work that you can show / advertise. It doesn't have to be professional work, I would assume most people will not go in depth before calling you if it's relevant to them.