As a new dentist, your main source of professional insecurity is probably a lack of experience. It's called dental "practice" for a reason and as you progress in years and experience your confidence will grow. In the meantime, your "reputation" will be built upon your personal integrity, along with the individualized care and attention you give your patients. Of course, great communication skills are essential to building trust with patients, and the more you are able to inform and educate patients, the more they will feel comfortable with you and your skills. Always "inform, before you perform", and you will find that you and the patient will be on the same page.
Fortunately, patients perceive new graduates as having been trained in the latest dental techniques. If you can communicate a sense of expertise on cutting-edge treatments, your reputation in the eyes of your patients will be greatly enhanced. Patients will definitely begin to trust you if they feel you are providing them with state-of-the-art treatment. Your reputation will grow in proportion to the level of confidence you express in your treatment plan presentations and the reasonable options you are able to offer your patients. Reputations are built this way over time, and there is a truism that states that a good reputation can take years to build, and a few minutes to destroy. So focus on patient communication and developing trust.
In terms of expertise, a marvelous way to grow your confidence is to devote yourself to life-long learning. Patients expect and appreciate this, and a great way to emphasize your devotion to excellence is to discuss the latest dental continuing education you've taken with your patients. They love to hear about the latest research and advances in dentistry that will benefit them. If you can express your knowledge and enthusiasm for newer, more conservative, and more predictable procedures your reputation will be that of a dedicated and knowledgeable dental professional. That reputation is one that will carry forward and will only be enhanced as your clinical skills develop. A wide range of courses to help you achieve this are available for immediate download at Dental Didactics CE
Being patient-oriented and concerned with predictable clinical outcomes, rather than having an emphasis on production and profitability, will definitely build your reputation as a true professional who puts the patient first. Patients have an excellent sense of when they are being presented with a "sales pitch" for services, and have treatment plans presented that reflect aspects of "over-treatment". Again, patients will assign motivations and intentions to you based upon their perceptions of your reputation, and no amount of additional short-term production will be as valuable as having a reputation for ethical evaluation of what treatment is truly ideal and necessary.
When patients are treated well, with individualized and personal care, they will develop loyalty to you as their dentist, and will subsequently feel confident and happy recommending you to their friends and family. Those referrals, generated from within your practice, are the ultimate measure of success; for at that point you have earned the trust of your current patients, and your reputation precedes you in the minds of your future patients.