If a person calls my business and no one answers the phone, the call gets automatically forwarded to a virtual receptionist service. A live person working for the service answers the phone call and takes a message for my company. The person answers incoming calls from a variety of businesses that all use this answering service. If the call is forwarded from my office number, the receptionist knows to answer for my company. I rarely get calls on shabbos however when yom tov is on a weekday there are many calls. I have instructed the service to simply inform callers that our office is closed and will reopen the next business day. In practice I see that messages are taken, i.e. name and number of caller. This is for a law office so the calls do not result in any income directly. Some messages may prevent a loss of income. Is there a problem of having a person perform work for me on shabbos/yom tov, possibly even a nonreligious jew? Although, the person answering the call is working for the answering service not directly for me.
Your question is discussed in the sefer Commerce and Shabbos on pg. 168. He says there that, if the company will inform the company answering the calls that they are contractually in no way obligated to answer any phone calls during Shabbos of Jewish holidays, and that if they don’t answer phone calls on those days, they will not be held responsible. Then any phone calls that they take, are for thier own benefit, and it is permitted.