A designated DPO is a ROLE not a person, that's a huge difference. Just like a security officer in a small company is a role assigned to someone who most likely has other duties too in a large company it will be a dedicated person (and in a really large company there might even be more people working in a team under a CISO or something to that effect). So 'designated' means that the role has to be assigned to a person, it does not say 'dedicated' where you'd have to have a person whose exclusive job is DPO.

So, DPO is not necessarily a person with no other duties. In most smaller organizations that deal with sensitive data the DPO role will be shared with the CCO (Chief Compliance Officer), only at a certain scale of processing and with certain data would you need to budget for a dedicated DPO from day one, but presumably your business plan will also foresee in other things such as office space, computers and so on. Certain businesses come with implied costs.