If the recipient ignores your letter, you have the option to commence legal proceedings. However, you should give the recipient a reasonable amount of time to comply with your request.
What constitutes a reasonable timeframe depends on:
Delivery method: Email or a process server can deliver a letter immediately, but a standard postal service will take longer. In this case, three to five business days to respond is reasonable.
The behavior or activity you want to be stopped: It might take time for the recipient to remedy the situation depending on the activity or behavior that needs to stop. For example, if they're running an ad online that illegally contains your company logo, they may need time to contact the advertising company and remove the ad.
Response method: If you mailed your Cease and Desist Letter to a collection agency, they would most likely respond by sending you a letter in return. Since it took time for them to receive your letter, it's only fair to give them the same amount of time to send their response before you proceed further.