What is the ruling on eating the slaughtered animals of Ethiopian Christians who mention over them, "In the name of the Father, the Son, and the Holy Spirit"?

The animal slaughtered by a person of the Book is permissible under two conditions: that he slaughters it as a Muslim would, by cutting the windpipe and esophagus and letting the blood flow, and that he does not mention any name other than Allah's, such as the Messiah. If it is known that he mentions a name other than Allah's, like "In the name of the Father, and the Son, and the Holy Spirit," then his slaughtered animal is not permissible. However, if what was mentioned upon it is unknown, then the default rule for their slaughtered animals is permissibility.