When negotiating with a prospective buyer, there have been a couple of times I was asked if I own the matching Twitter handle to a domain name I have. In both cases, I did not own the Twitter nickname and it did not impact the negotiation.
I know there are some people who will try to secure the matching Twitter name to their domain name. I think it could enhance the value of domain name if the matching Twitter handle is also managed, but I have never done this before. My feeling is that someone could then ask about Facebook, Instagram, and other social media handles. In addition, most of the Twitter handles matching important domain names were claimed long ago and would take a real effort to secure.
It would be interesting to know how many domain investors secure Twitter handles / nicknames for domain names they own. It would be great for people to share insight in addition to responding to the poll below: