Professors generally appreciate when students introduce themselves during office hours, especially in smaller departments where relationships can develop quickly. The willingness of professors to engage varies by individual and university culture, but many enjoy chatting with students if approached politely. It's important to respect their time and visit during designated office hours or schedule an appointment via email. Engaging with professors can foster a positive relationship and enhance the learning experience. Overall, taking the initiative to connect is often well-received when done appropriately.