The question is can i marry a woman who does not pray but bear Muslim name?

 The question is can i marry a woman who does not pray but bear Muslim name?

Alhamdulillah,it is not permissible to marry a woman or man who does not pray because that person is not a believer.

Allah says,

Al-Baqarah 2:221

وَلَا تَنكِحُوا۟ ٱلْمُشْرِكَٰتِ حَتَّىٰ يُؤْمِنَّۚ وَلَأَمَةٌ مُّؤْمِنَةٌ خَيْرٌ مِّن مُّشْرِكَةٍ وَلَوْ أَعْجَبَتْكُمْۗ وَلَا تُنكِحُوا۟ ٱلْمُشْرِكِينَ حَتَّىٰ يُؤْمِنُوا۟ۚ وَلَعَبْدٌ مُّؤْمِنٌ خَيْرٌ مِّن مُّشْرِكٍ وَلَوْ أَعْجَبَكُمْۗ أُو۟لَٰٓئِكَ يَدْعُونَ إِلَى ٱلنَّارِۖ وَٱللَّهُ يَدْعُوٓا۟ إِلَى ٱلْجَنَّةِ وَٱلْمَغْفِرَةِ بِإِذْنِهِۦۖ وَيُبَيِّنُ ءَايَٰتِهِۦ لِلنَّاسِ لَعَلَّهُمْ يَتَذَكَّرُونَ 

English - Sahih International

And do not marry polytheistic women until they believe.[1] And a believing slave woman is better than a polytheist, even though she might please you. And do not marry polytheistic men [to your women] until they believe. And a believing slave is better than a polytheist, even though he might please you. Those invite [you] to the Fire, but Allāh invites to Paradise and to forgiveness, by His permission. And He makes clear His verses [i.e., ordinances] to the people that perhaps they may remember.

English - Tafsir Ibn Kathir (Abridged)

<h2>The Prohibition of marrying Mushrik Men and Women</h2>

Allah prohibited the believers from marrying Mushrik women who worship idols. Although the meaning is general and includes every Mushrik woman from among the idol worshippers and the People of the Scripture, Allah excluded the People of the Scripture from this ruling. Allah stated:

مِنَ الَّذِينَ أُوتُواْ الْكِتَـبَ مِن قَبْلِكُمْ إِذَآ ءَاتَيْتُمُوهُنَّ أُجُورَهُنَّ مُحْصِنِينَ غَيْرَ مُسَافِحِينَ

((Lawful to you in marriage) are chaste women from those who were given the Scripture (Jews and Christians) before your time when you have given their due dowry, desiring chastity (i.e., taking them in legal wedlock) not committing illegal sexual intercourse.) (5:5)

`Ali bin Abu Talhah said that Ibn `Abbas said about what Allah said:

وَلاَ تَنْكِحُواْ الْمُشْرِكَـتِ حَتَّى يُؤْمِنَّ

(And do not marry Al-Mushrikat (female idolators) till they believe (worship Allah Alone).) "Allah has excluded the women of the People of the Scripture." This is also the explanation of Mujahid, `Ikrimah, Sa`id bin Jubayr, Makhul, Al-Hasan, Ad-Dahhak, Zayd bin Aslam and Ar-Rabi` bin Anas and others. Some scholars said that the Ayah is exclusively talking about idol worshippers and not the People of the Scripture, and this meaning is similar to the first meaning we mentioned. Allah knows best.

Abu Ja`far bin Jarir (At-Tabari) said, after mentioning that there is Ijma` that marrying women from the People of the Scripture is allowed, "`Umar disliked this practice so that the Muslims do not refrain from marrying Muslim women, or for similar reasons." An authentic chain of narrators stated that Shaqiq said: Once Hudhayfah married a Jewish woman and `Umar wrote to him, "Divorce her." He wrote back, "Do you claim that she is not allowed for me so that I divorce her" He said, "No. But, I fear that you might marry the whores from among them." Ibn Jarir related that Zayd bin Wahb said that `Umar bin Khattab said, "The Muslim man marries the Christian woman, but the Christian man does not marry the Muslim woman." This Hadith has a stronger, authentic chain of narrators than the previous Hadith.

Ibn Abu Hatim said that Ibn `Umar disliked marrying the women from the People of the Scripture. He relied on his own explanation for the Ayah:

وَلاَ تَنْكِحُواْ الْمُشْرِكَـتِ حَتَّى يُؤْمِنَّ

(And do not marry Al-Mushrikat (female idolators) till they believe (worship Allah Alone).)

Al-Bukhari also reported that Ibn `Umar said, "I do not know of a bigger Shirk than her saying that Jesus is her Lord!"

Allah said:

وَلأَمَةٌ مُّؤْمِنَةٌ خَيْرٌ مِّن مُّشْرِكَةٍ وَلَوْ أَعْجَبَتْكُمْ

(And indeed a slave woman who believes is better than a (free) Mushrikah (female idolators), even though she pleases you.)

It is recorded in the Two Sahihs that Abu Hurayrah narrated that the Prophet said:

«تُنْـكَحُ الْمَرْأَةُ لِأَرْبَعٍ: لِمَالِهَا وَلِحَسَبِهَا وَلِجَمَالِهَا وَلِدِينِهَا، فَاظْفَرْ بِذَاتِ الدِّينِ، تَرِبَتْ يَدَاك»

(A woman is chosen for marriage for four reasons: her wealth, social status, beauty, and religion. So, marry the religious woman, may your hands be filled with sand (a statement of encouragement).)

Muslim reported this Hadith from Jabir. Muslim also reported that Ibn `Amr said that Allah's Messenger ﷺ said:

«الدُّنْيَا مَتَاعٌ، وَخَيْرُ مَتَاعِ الدُّنْيَا الْمَرْأَةُ الصَّالِحَة»

(The life of this world is but a delight, and the best of the delights of this earthly life is the righteous wife.)

Allah then said:

وَلاَ تُنكِحُواْ الْمُشِرِكِينَ حَتَّى يُؤْمِنُواْ

(And give not (your daughters) in marriage to Al-Mushrikin till they believe (in Allah Alone).) meaning, do not marry Mushrik men to believing women. This statement is similar to Allah's statement:

لاَ هُنَّ حِلٌّ لَّهُمْ وَلاَ هُمْ يَحِلُّونَ لَهُنَّ

(They are not lawful (wives) for them, nor are they lawful (husbands) for them.) (60:10)

So we know anyone who does not pray intentionally is a Disbeliever.