The Shahada names Prophet Muhammad (PBUH) because its two clauses serve two different purposes: the first identifies the only One worthy of worship, and the second identifies the final messenger whose revealed way is to be followed. Naming Muhammad (PBUH) does not make him a partner in worship; it is part of obeying Allah.
What the Shahada means
The Shahada is commonly expressed as: "I bear witness that none has the right to be worshipped except Allah, and I bear witness that Muhammad is the Messenger of Allah." The Quran teaches both of these meanings clearly, though the exact combined liturgical formula is established through the Prophet's (PBUH) Sunnah and the practice of the Muslim community.
"Islam is built upon five: testifying that none has the right to be worshipped except Allah and that Muhammad is the Messenger of Allah..."
Sahih al-Bukhari 8; Sahih Muslim 16
The first clause is about worship: no one deserves worship in truth except Allah. The second clause is about messengership: Muhammad (PBUH) is the messenger sent by Allah, so his teaching, law, and guidance are to be accepted.
Naming Muhammad does not make him divine
The Shahada does not say that Muhammad (PBUH) is worshipped, divine, or a partner with Allah. It says that he is "the Messenger of Allah." A messenger is obeyed because Allah sent him, not because he shares in Allah's lordship or worship.
"He who obeys the Messenger has obeyed Allah..."
Quran 4:80
The Prophet (PBUH) himself was commanded to declare his humanity and servitude to Allah:
"Say, 'I am only a man like you, to whom has been revealed that your god is one God...'"
Quran 18:110
Why Muhammad is mentioned specifically
Prophet Muhammad (PBUH) is named because he is the final messenger and the messenger sent to this final prophetic community. Entry into that community entails accepting the messenger through whom Allah sent the final revelation.
"Muhammad is not the father of any one of your men, but [he is] the Messenger of Allah and seal of the prophets..."
Quran 33:40
"Say, [O Muhammad], 'O mankind, indeed I am the Messenger of Allah to you all...' So believe in Allah and His Messenger, the unlettered prophet... and follow him that you may be guided."
Quran 7:158
This is not unusual: accepting Allah includes accepting the messenger Allah sends. One cannot claim to accept the final revelation while rejecting the prophet who delivered it.
Belief in all prophets remains required
The Shahada's mention of Muhammad (PBUH) does not erase the other prophets. Muslims must believe in all prophets whom Allah sent, including Abraham, Moses, Jesus, and others. The Quran says:
"The Messenger has believed in what was revealed to him from his Lord, and [so have] the believers. All of them have believed in Allah and His angels and His books and His messengers, [saying], 'We make no distinction between any of His messengers.'"
Quran 2:285
"We make no distinction" means Muslims do not accept some prophets while rejecting others. It does not mean every prophet had the same rank, but it does mean every true prophet must be believed, honored, and accepted as a messenger of Allah.
In short, the Shahada singles out Muhammad (PBUH) because he is the final messenger whose revealed way Muslims now follow. It affirms pure worship of Allah alone while also affirming belief in all of Allah's messengers. For related doubts, see the topics on the finality of prophethood and the Muslim belief in Jesus and earlier prophets.