who is responsible in my company for ESG or sustainability

Usually the board of directors, not a separate ESG team

Responsibility for sustainability lies with the board as a whole in virtually all questionnaires, not with a separate officer. A "sustainability manager" or "ESG coordinator" may handle implementation, but the question about board responsibility concerns governance: who directs, who approves, who reports. That follows the same logic as the composition of the board of directors — the client wants to know if there is oversight, not who types the report.

In a sole proprietorship or small private company without a formal board, the answer is often simply the owner or director. Larger companies sometimes designate a specific board member with sustainability in their portfolio; you can fill that in if it is accurate, but do not invent a position that does not exist. If the company has no documented allocation of responsibility, then "no" or "not assigned" is a valid answer — better than naming a person who cannot be verified.

VSME basic module and the CSRD as framework

The EFRAG VSME standard, the voluntary basic module for non-listed SMEs, asks in the governance section who within the company is responsible for sustainability policy and reporting; that is usually the question that comes back in client portals. Directive (EU) 2022/2464, the CSRD, imposes this governance obligation on the reporting company itself; the SME company that completes the questionnaire often receives the question passed through because its client must substantiate this for its own supply chain reporting. A similar structure — tracing responsibility to a concrete body or process rather than a job title — you see reflected in the answer to whether there is a procedure for conflicts of interest: there too what counts is whether it is documented, not who happens to do it.