Tangentially, how do you get into a PhD program without any academic letters of recommendation (if, for example, you've been working in industry for a few years)?
Pretty similar to all the other suggestions - make contact with somone in the department who works on what you want to do your PhD in. Talk to them, find out what you need to do to get them to supervise you. If they won't ask for another name.
And be persistent.
And be able to show your skillz, to catch their eye. Otherwise you're just a name that wants special attention in a (potentially) large, seething crowd.