Here is some beautiful Muslim names, there are of course much more but these are the most common names take a look:

Note: The spelling of these names in English or any other languages other than Arabic may differ a little bit.

Men names:

Muhammad = محمد , The name of the Final Prophet and Messenger of Allah (SWT) to mankind and the  worlds, the name means the praised one, there is also a chapter in the Quran named Muhammad, it is mentioned 4 times in the Holy Quran this name is also mentioned in the Hebrew Bible the old Testement  מַחֲמַד , in the Song of Solomon chapter 5:16, the name of the Prophet even mentioned in the old Hindu scriptures (Click the link to go to the Hinduism Page to see the references if you like).

Ahmad = أحمد  Synonyms for Muhammad, it is also the name which refers to Prophet Muhammad (PBUH).

Adam =  ادم , the name of the first man Allah (SWT) created and it means in Arabic clay.
Ibrahim =  أبراهيم , the name of the great Prophet Abraham in the Arabic language.
Ismail = أسماعيل , Known in English as Ishmael, he is a great prophet of Allah, he is the first son of prophet Ibrahim, together with his father they have build the first place ever to worship God alone and that place is the Qa’ba in Mecca and he is the great grand father of prophet Muhammad (PBUH).
Ali = علي , the name of the cuisine of the Prophet and one of the greatest Heroes of Islam he was also the fourth Khlif ,the name means “high or Nobel” , Ali was the Husband of Fatima the daughter of the Prophet, they had the two beloved grandsons of the Prophet, Hassan and Husain.
Musa = موسى , the name of the great Prophet of Allah known in English as Moses.
Haroon = هارون , a great prophet of Allah, he is known in English as Aaron, he is the brother of Prophet Musa (Moses).
Isa = عيسى , the name of Prophet Jesus in Arabic.
Hassan = حسن , the first grandson of the Prophet from his daughter Fatima and her husband Ali the cuisine of the Prophet, the name means good or beautiful or alright.
Husain = حسين , the name of the second grandson of the Prophet from his daughter Fatima and his cuisine Ali he is one of the great martyr for Islam.
Abdu Allah = عبد الله , it means the worshiper or the servant  of Allah.
Abdu Al Rahmaan = عبد الرحمن , it means the worshiper of the Merciful One .
Yusuf =  يوسف , is a great Prophet of Allah, known in English as Joseph, he was at the time of the Faros, he was a great prophet and exceptionally good looking.
Idris = أدريس , a great prophet, he was the sixth generation grandson of Adam, Allah Almighty said that He elevated him into a high place and describes him as righteous and patient, he was the last prophet before prophet Noah. 
Nooh = نوح ,  a great prophet known in English as Noah know for the flood story in the Quran.
Zachariah = زكريا , name of a great Prophet of Allah, he is the father of Yehya .
Yehya = يحيى , the name of a great Prophet of Allah he is know in English as John the Baptist.
Dawood = داود , is a great prophet of Allah known in English as David.
Sulaiman = سليمان  , is a great prophet of Allah known in English as Solomon.
Ayoob = أيوب  , a prophet of Allah known in English as Job.
Yaqoob = يعقوب , is a prophet of Allah known in English as Jacob.
Hamza = حمزة , means a lion who is about to attack, it is the name of the uncle of the Prophet, who was one of the great Heroes of Islam, he really lived up to that name.
Yasir =  ياسر , the first martyred Man who was killed in because of his belief in Allah and in Islam.
Bilal = بلال , the first slave who rejected Idolatry and believed in the Prophet and in Islam, he was originally from Abyssinia in Africa, he suffered a lot before he was freed by the Prophet and his companions.
Omar = عمر , a close companion of the Prophet and the father of Hafsa one of the Prophet’s  wives and  he was the second Khalifa. 
Uthman = عثمان , is a close companion of the Prophet and the husband of his daughter.
Salih = صالح , a great prophet of Allah, he is mentioned in the Qur’an.
Qasim = قاسم  , the name of the son of the Prophet who died when he was a child.
Zaid = زيٌد  , the name of the adopted son of the Prophet, he was a black child slave, who was given as a present to the prophet but the prophet freed him and adopted him as his own son, his name is mentioned in the Qur’an.

Women names:

Miriam =  مريم , the name of the Mother of Jesus in the Arabic language there is a whole chapter in the Quran, named chapter Miriam in the homer of the mother of Jesus and she is the only woman in the quran which is mentioned by name.
Aminah = امنة , at peace ( for  female) the name of the mother of Prophet Muhammad (PBUH).
Khadijah = خديجة , the name of the beloved first wife of the Prophet and the first to embrace Islam.
Fatimah=  فاطمة , the name of one of four daughters of the Prophet (nick named Al Zahra’a which means the flower).
Ruqaiah =  رقية , the second daughter of the Prophet.
Zainab =  زينب , the name of the daughter of Fatimah.
Aisha =  عائشة , the name of the last wife of the Prophet and the daughter of his close friend and follower.
Safiah = صفية , she is one of the prophet wife’s, she is the daughter of the chief Jewish leader she fought to protect the back of the Muslim army against her own people.
Heleemah = حليمة  , when the prophet was a baby and his mother died this woman breast fed him.
Sumaiah =  سمية , the first martyred Woman who was killed because her belief in Allah and in Islam.
Hafsa = حفصة , one of the prophet wives and the daughter of his close companion Omar the second Khalif.
Huda =  هدى , a beautiful name it means Guidance.
Leila = ليلى  , another name which is very known and beautiful it is Arabic and International name.