Is it obligatory to take the final step of entering Islam and changing one's name to an Islamic name like "Ismail" after being convinced of it?

One must follow the truth, even if it goes against what one was brought up with. Islam is the true religion that came as the seal of all religions and laws. Believing in it does not mean cutting oneself off from righteous roots; rather, it entails believing in all prophets and heavenly books before they were distorted. And whoever believes in Jesus and then in Muhammad, peace be upon him, will have a double reward. Therefore, it is essential to embrace Islam for the happiness it brings and for drawing closer to God. As for the name, it is permissible to keep it unless it contains polytheism or disbelief, and the name Ismail is very suitable.