There is a fine balance to be made between a lack of confidence and an abundance of confidence. If you have too little confidence in yourself and your work, you wind up getting your foot in the door less often and you wind up making less as a result in the long run. If you have too much confidence however, it can wind up turning off potential clients and similarly giving you less money. The appropriate approach to this job is to be humble, but self-confident. You would hardly claim that your work is the best ever – there is always going to be someone who is better than you (and as a result giving you motivation to do better) – but you want to at least establish, both through how you present your work and the quality of your work itself, that there is a ton of value to be gained from them using your logos.
In my history in graphic design, I have actually seen examples of both, unfortunately enough. The first example is someone I knew when first starting out. He was really mouthy, had a lot of confidence in himself. He was usually nice – probably one of the nicest people in the industry I’ve met in most contexts – but in the context of the industry? He was cutthroat, and would happily tear your work apart (not literally, thankfully). He had some initial success, and took this to mean that he could behave in that way and have success. As such, he kept going further and further down that path, and unfortunately, he wound up burning all too many bridges and finding himself with not much of a career leftover. He still does some work, but less work than he deserves with his talent. The other one? It’s me! I used to have so little confidence in my work, especially when I was young. I had some nasty anxiety and self-pity, so it limited my ability to expose myself. A solid family and friend support system helped me out and got me where I am today.