Yes, yes, and yes. Asking people to make comments or connections can feel forced. For me, this is most often true when there is a grade attached to activities intended to build community. Sometimes the lurking without comment can build a quiet community, too. Do you think people need to comment on each other's padlets in your activity? Do people need to make visible connections to build community? Maybe this is a broad question for the open forum.
I'm guessing any single community building activity is most often a starting place, but having the activity happen in concert with many other pieces (like adequate facilitator presence, opportunities for vulnerability and story sharing, engaging small group activities, multiple ways to connect, etc.) may inch the group toward community. Or not! A lot probably depends on the group, too.
Your activity reminded me of a comment that came up during our last institutional teaching chat on Indigenization and Assessment. I went back to the notes to quote it. Someone said: "Western values have been driving our pedagogies. What else is out there?" An Indigenous scholar in our group said, "sharing, relationships, listening, and connecting to land and people using an individual-family-community-nation framework." For me, your proposed activity aims to do just that. You explore the name and its affects on the individual, and then aim to connect it to family/community/culture.