Is it permissible to say "Allahumma Salli ala Muhammad" (O Allah, send blessings upon Muhammad) upon hearing someone call another person whose name is Muhammad?

Prayers and peace be upon the Prophet, may Allah’s prayers and peace be upon him, are desirable at all times, and Allah Almighty commanded this in His saying: "Indeed, Allah and His angels send blessings upon the Prophet. O you who have believed, ask [Allah to confer] blessing upon him and greet him with [due] salutation." And there are hadiths that encourage this, such as: "Whoever sends blessings upon me ten times in the morning and ten times in the evening will receive my intercession on the Day of Resurrection," and "When you hear the muezzin, say what he says, then send blessings upon me, for whoever sends one blessing upon me, Allah will send ten blessings upon him," and "The miser is one in whose presence I am mentioned, and he does not send blessings upon me," and "May the nose of a man be rubbed in dust, in whose presence I am mentioned, and he does not send blessings upon me." Sending prayers upon the Prophet when his name is mentioned, even if the name Muhammad is used for someone else, there is no harm in sending prayers upon him, and you will be rewarded for it.