The sysadmin role is a powerful role that has administrative control over the entire SQL Server instance. Members of this role can perform any action on the SQL Server, including altering server settings, creating, modifying, or deleting databases, and managing security. So you need to determine who or what staff that falls under this criteria. Also important to be cautious about who you assign this role to, as it grants significant privileges that can impact the security and stability of your SQL Server environment. In your case, probably a senior IT support staff or System Administrator and possibly SQL Server service accounts may require a sysadmin role.
To your second question, you can collectively call your SQL servers "a cluster of servers". There isn't a specific name for it, just depends on context and level of technical detail you want to convey.
Hope this helps