Techie's Perception

After working with a IT services company for 15 years, I have joined a MAFANGI company as a Tech Lead. It's been two months now. One of the feedbacks I have received is that I don't exude confidence.

I am in a new and demanding world and learning many new things as the domain is new to me. In my head, I am improving every day and use my skills well in new domain. However, with my experience level, I feel I should exude confidence (but not fake it).

What can I do to improve? Working consciously on Communication Skills is one thing on my mind. I am also a bit bad at marketing my self. Can someone please share their experience in similar situation?