According to some practitioners of VoC, they will tell you that the entire product development team is responsible for VoC, that it takes a cross-functional team to sustain the integrity of VoC for the duration of the product cycle. They will put the responsibility on a cross-functional core team, tiger team, or VoC steering committee of 5–7 individuals from marketing, engineering, manufacturing, service and repair, and finance to ensure that the VoC is obtained, processed, and included in your new product.
While I applaud their desire to make sure that VoC is everyone's responsibility, what I have found in most organizations is that when something is "everyone's responsibility", no one ends up being "responsible".
I believe the responsibility of VoC falls squarely on whoever is responsible for product management. That could be a product manager, it could be a product marketing manager, or it could be a marketing manager. It could also be the owner of the business, depending...