This is difficult to answer authoritatively without some context. People's titles will often change depending on what line of business they are in, even if they are doing the same process. You will often see the suffix '-ee' used to designate someone an action is being done to. I'll give you some examples:
Renting an apartment:
Who asks for the service? Lessee.
Who receives the request for a property? Rental Company Representative (or similar)
Who carries out the service? Lessor
Note that the person who receives the request is often the person who carries out the request, or a representative on their behalf. This position can come with MANY titles.
At a restaurant:
Who asks for the service? Patron
Who receives the request for food? Waiter/waitress
Who carries out the request? Chef, cook, and so on
One company contacting another for a service:
Who asks for the service? The Client
Who receives the request for service? Service Representative, Outreach Coordinator, Representative, and so on
Who carries out the service? <Some title for the type of service> for example:
Computer repair -> Computer repair technician
Building repair -> Structural engineer, contractor
Consulting -> Consultant
Audit -> Auditor, Assurance professional
There are many, many different words to describe the situation, so more information is truly helpful to answer the question. Also note that "the Client" or other abstractions of the client's name are often used in reports and proposals after establishing in the first few lines who "the Client" is. Example:
"Stonewater International Mining Corporation, hereafter known as 'the client' or 'Stonewater International' is ..."