All perfect praise be to Allah, The Lord of the Worlds. I testify that there is none worthy of worship except Allah, and that Muhammad is His slave and Messenger.
Whenever a Muslim hears the name of the Prophet he/she should ask blessings and peace of Allah for him even during the Friday sermon, but in a low voice.
Abu Hurayrah narrated that the Prophet said: “May that person be humbled in whose presence my name is mentioned but he does not invoke blessings upon me.” [At-Tirmithi]
Abu Hurayrah also narrated that the Prophet said: “Whenever anyone sends Salam to me (invokes blessings upon me), Allah will restore my soul to me, till I respond to his invocation.” [Abu Dawood with sound chains]
So whoever hears the Prophet’s name (Blessings and peace of Allah be upon him), he should invoke blessings upon him even if it is during the Friday (Jumm‘ah) sermon.
For more benefit, please refer to Fataawa 84766, eighty times on Friday">307192, 84530, and 82212.
Allah knows best.