the picture thing is to avoid idolatry, which was the main type of religion in the region at the time Islam was beginning. people were used to worship to (or via) visual depictions of gods, so a ban on visual representations of people was an effort to avoid people falling into old habits.

that's why currently an overwhelming majority of Muslims don't care about depictions of people in general, but they still don't allow the prophet or god to be depicted (god isn't supposed to have any physical form anyway) because that would be too close to idolatry.

kind of the opposite approach of christians with pagans, where christians appropriated pagan symbols to make Christianity more appealing, media were concerned with differentiating themselves from other religions.

uttering names isn't taboo in Islam like it is in Christianity. while some Christians avoid saying God, Jesus or the like, Muslims are encouraged to use god's name frequently. however they're not allowed to call people certain names reserved for god alone, but that isn't the case for the prophet. so it's considered sort of a tribute or a sign of respect to name people after the prophet.

interesting fact, Muhammed isn't the prophet's only name, so while this is the most common name in the world, the number of people named after the prophet is even higher, because it includes some other names, most common after Muhammed being Ahmed.