Or even an " executive pastry chef " while you're at it. If you own your shop / kitchen and/or supervise or have administrative authority, you can stick executive in front of it.
Chef coats can be bought anywhere and have anything written on them, they are a kitchen appropriate clothing. It shows you don't work your oven in dirty clothes you just did construction work in. They should be used tought not just paraded around.
The prestige people put into them is on a personnal level really. If you have one from " Four-Seasons " because you attended culinary school for so many years and busted your butt to get there or if you bought one and had it embroided to say " little corner bakery, my name here ". Im sure to the wearer the feel of pride very similar. At the end it really just says " hey, im a professionnal and I don't bake in my pj's. "