My uni did, but my uni was different in that this course spent 3 years getting us ready for the industry upon graduation. Not like your standard 'find yourself' and dissertation degree. May well be different now, but the the course I did was one of the first like this in the country. We had modules on freelancing, business, building portfolios, interview techniques, live projects, guest speakers, pitching, and 1 big one on branding ourselves. We had to create ourselves a logo, stationary, design a website (in Flash but still) then have all of this stuff displayed in our final year degree show. Was pretty cool actually.
I treat my company as a brand in the sense that I've got my logo, branded stationary, followed through into quotes, invoices and receipts, Ts&Cs and website. With regards to me, I'm just me. I don't turn up to interviews in suits, I wear what I', comfortable in. I think I'm naturally groomed. I don't spend every night plucking nose hair or shaping eyebrows put it that way. Some days I sport stubble .. somedays I don't.
Same with answering the pone and email. I answer and reply as me, nothing special.