Q. Why can't Muslims?

When Muslims have the best holy book in their hand, why should they convert?

A Muslim is one who submit to the will of GOD(Allah in Arabic) and actually there is no conversion in eitherway, it is the understanding of GOD, the better way.

a person with a Muslim name can convert to any religion but a Muslim who really believes and practice will never convert and he cannot convert.

Let's talk frankly. Almost never do non-Muslims study Islam until they have first exhausted the religions of their exposure. Only after they have grown dissatisfied with the religions familiar to them, meaning Judaism, Christianity and all the fashionable "-isms"—Buddhism, Taoism etc —do they consider Islam.
Perhaps other religions do not answer the big questions of life, such as "Who made us?" and "Why are we here?"
So let us return to the topic: Why Islam? Why should we believe that Islam is the religion of truth, the religion that possesses the pure and final revelation?
Oh, just trust me.
Now, how many times have you heard that line? A famous comedian used to joke that people of different cities cuss one another out in different ways. In Chicago, they cuss a person out this way, in Los Angeles they cuss a person out that way, but in New York they just say, "Trust me."
So don't trust me—trust our Creator. Read the Qur'an; read books and do dome study on it. But whatever you do, get started, take it seriously, and pray for our Creator to guide you.