What team structure should an SEO company have?
Whatever its size, it should cover six functions, each with a named person accountable for it on your account: strategy, technical work, content, links and outreach, measurement and reporting, and day-to-day client contact. Job titles vary and one person can hold more than one function in a small company. What matters to you is that every function has an owner, that the owners are coordinated, and that someone covers when a person is away.
The six functions
Strategy decides what the work is for: it reviews the site and the competition, sets priorities, and can explain why each task is on the list.
Technical work covers how the site is crawled, rendered, and indexed: redirects, canonical tags, structured data, speed, and site architecture. It overlaps with web development, so the person holding it has to work well with your developers or have development support in the company.
Content plans which pages to create or rewrite, briefs the writers, and checks drafts for accuracy and for the search each page is meant to answer.
Links and outreach earn mentions and links from other sites and keep track of what has been earned.
Measurement sets up and checks the tracking, compares results with the baseline, and turns data into findings.
Client contact keeps you informed, collects the information the team needs from you, and is the person you call when something needs a decision.
Small teams and large ones
In a small company, one person may hold strategy and client contact, or technical work and measurement. That is fine as long as each function is actually done and someone covers it during absences. The question to ask a small company is not whether it has six people, but who holds each function for your account and who steps in when that person is unavailable.
Larger companies organize in different ways, and two are worth knowing. In the first, a small team serves a set of clients and covers several functions together, which can keep communication close. In the second, specialist departments each handle one function across many clients, which offers depth in each discipline but needs someone to coordinate them for your account. Neither is better in itself; ask how coordination works in the one you are offered.
Who works on your account
The people in the sales meeting are not always the people who do the work. Ask for the names and roles of the people who will work on your account, how much of their time it will get, and who is accountable for each function. Then give each person the access their function needs, not more. Search Console, for example, distinguishes owners, full users, and restricted users in its permissions settings: the technical lead needs different access from the content writer, and none of them needs to own your accounts.
Asking for names, not job titles
Ask who holds each of the six functions for your account, who covers each one during absences, which functions are handled by subcontractors, and how the people involved coordinate. A company that can answer with names has a structure; one that answers only with job titles may not have decided yet.