I really wish I could finish it but there are so many variables. My thoughts would center on her habits - her work schedule, etc. If she worked primarily mornings, then I could see a blue collar type (construction, self-employed, etc), perhaps with an (unknown) past violent and/or sexually deviant history, coming in every morning very early for coffee and a doughnut and shooting the breeze with her (or more importantly, shooting the breeze with others about her). He would probably be a rugged, minimally educated, salt of the earth type in his 40s-50s either divorced or single with a history of unstable sexual relationships or domestic violence. Maturity level and IQ are probably low too, and he has a short fuse.
Or, if she worked primarily mid shift or evenings, it could be someone younger (25-35) with a shy and unstable presence - meaning lack of a steady job, unkempt, loner, etc. Any hint of positive attention would get his fantasy narrative going. Think borderline personality disorder - friendly until someone sets him off via rejection or making him feel dumb, etc. May have past run ins with the law but perhaps not of the violent type.
Either way, if I were the police, I would be scanning every credit/debit card purchase over the last few weeks to few months and try to find a corresponding pattern - particularly matching name to DMV photo to car type. He most certainly had to purchase something there at some point, and the likelihood that he always used cash is slim.
All of the above is speculative and IMO, and certainly open to feedback/criticism, and even adding to the hypothesis if you wish.