Unless you're sending from your email address or through your mobile device (via a desktop app), recipients won't have any way to know that it's you sending the message. You should always include your name to let them know who they're getting a random text message from. This is especially true if you're using a temporary number that a recipient may mistake for spam.
Remember that none of the options are completely anonymous. Some options will require more effort than others to track your IP address, but they're not anonymous.