Most online texting platforms operate by acting as a gateway between a web interface and a cellular network. While they hide your personal phone number from the recipient, they rarely provide true anonymity from the service provider itself. Most platforms log IP addresses, timestamps, and metadata to comply with anti-spam laws and prevent harassment.
For the curious reader, the goal is usually a balance between discretion and reliability. Some services are free and easy to use but suffer from low delivery rates because carriers flag their numbers as spam. Paid services typically offer better delivery and more features, but they introduce a financial trail that can compromise the anonymity you are seeking.