Can she marry a Muslim whose family is Catholic? Can the children be named after his kaafir people?
Question

                Was to know if someone is marrying a Muslim convert, does it matter if his family is Catholic? Also, after getting married, can children take fathers last name which is a non-Muslim name?.
Praise be to Allah.Firstly: 
Islam forbids women to 
    marry non-Muslims. This is something on which there is consensus among the 
    scholars, with no difference of opinion on this ruling. 
Al-Qurtubi (may Allaah have 
    mercy on him) said: 
The ummah is unanimously 
    agreed that a mushrik cannot marry a believing woman, because that is, in a 
    sense, a humiliation of Islam. 
Tafseer al-Qurtubi, 
    3/72. 
See also the answers to 
    questions no. 69752, 
    6402 and 
    22468. 
It is permissible for a 
    Muslim woman to marry a Muslim whom Allaah has guided to Islam after he was 
    a kaafir, and it does not matter if his family is Catholic or follows some 
    other religion. It also does not matter if he became Muslim a long time ago 
    or if he entered Islam recently, but what does matter – and is of the utmost 
    importance – is that his Islam is genuine and he is not pretending to be a 
    Muslim so that he can marry a Muslim woman, as there have been cases where 
    men pretended to have entered Islam on the basis of conviction when that was 
    not the case. If this is found out to be the case, then such a person is not 
    to be treated as a Muslim.  
Shaykh ‘Abd al-‘Azeez ibn 
    Baaz (may Allaah have mercy on him) said: 
It is essential to 
    understand the Kalimah which is Laa ilaaha ill-Allaah. It is the best of 
    speech and is the basis of Islam. It is the first thing that the Messengers 
    (peace and blessings be upon them) taught to their people and it is the 
    first thing that the Messenger  (peace and blessings of Allaah be upon 
    him) taught to his people when he said to them: “Say Laa ilaaha ill-Allaah 
    and you will succeed.” Allaah says (interpretation of the meaning): 
“And We did not send any 
    Messenger before you (O Muhammad صلى الله عليه 
    وسلم) but We revealed to him (saying): Laa ilaaha illa Ana [none has 
    the right to be worshipped but I (Allaah)], so worship Me (Alone and none 
    else)”
[al-Anbiya’ 21:25].
Every Messenger said to his 
    people: “Worship Allaah, you have no other god but Him.” So it is the 
    foundation of Islam, and it is essential for the one who says it to 
    understand what it means. It means that there is none who is rightfully 
    worshipped except Allaah. There are conditions for that, which are: 
    knowledge of what it means, certainty and absence of doubt that it is true, 
    sincerity towards Allaah alone, belief in one’s heart and on one's lips, 
    love for that which it indicates of sincerity towards Allaah, acceptance of 
    that, submission to Him, belief in His Oneness, disavowal of shirk and 
    avoidance of worshipping anything but Him, and belief that such worship is 
    false. These are all conditions of saying Laa ilaaha ill-Allaah. It is said 
    by the believing man and woman whilst rejecting worship of anything other 
    than Allaah, submitting to the truth and accepting it, loving Allaah, 
    affirming His Oneness, being sincere towards Him, and not doubting its true 
    meaning. For some people say it but they do not believe in it, like the 
    hypocrites who say it whilst doubting it or disbelieving in it. 
So it is essential to know, 
    have certain faith, believe in it, be sincere, love, submit, accept and 
    disavow other gods.  
Fataawa al-Shaykh Ibn 
    Baaz (3/49, 50). 
For more details on the 
    conditions of bearing witness that there is no god but Allaah, with 
    evidence, please see the answers to questions no. 
    9104 and 
    12295. 
Secondly: 
After the Muslim woman 
    marries a Muslim man, their children are to be named after their father, and 
    it is not permissible to do otherwise, even if his family are kaafirs. Many 
    rulings are connected to this attributed, such as kinship, inheritance, and 
    whether marriage is permissible or not, and so on. Hence it is not 
    permissible to name a Muslim child after anyone but his father and family. 
    There are texts which speak in strong terms about this issue and state that 
    the one who goes against that is committing a major sin. 
It was narrated that Sa’d 
    ibn Abi Waqqaas and Abu Bakrah said: The Messenger of Allaah  (peace and 
    blessings of Allaah be upon him) said: “Whoever claims after having become 
    Muslim to belong to someone who is not his father, knowing that he is not 
    his father, Paradise will be forbidden to him.” Narrated by al-Bukhaari 
    (4072) and Muslim (63). 
And it was narrated from 
    Abu Dharr (may Allaah be pleased with him) that he heard the Prophet  
    (peace and blessings of Allaah be upon him) say: “Any man who knowingly 
    attributes himself to someone other than his father has committed an act of 
    kufr. Whoever claims to belong to a people to whom he does not belong, let 
    him take his place in Hell.” Narrated by al-Bukhaari (3317) and Muslim (61). 
     
Al-Haafiz Ibn Hajar (may 
    Allaah have mercy on him) said: 
This hadeeth shows that it 
    is haraam to deny a parentage that is known and to claim to belong to 
    someone else. 
Fath al-Baari 
    (10/308). 
It is not known that anyone 
    among the Prophets, Sahaabah, Taabi’een or scholars changed their names 
    because of their fathers or grandfathers being kaafirs. No wise man would do 
    that, because of the evil that results from that. 
Anyone who studies the 
    books of biography will find foreign names of fathers and grandfathers for 
    many of the Muslim scholars, when Allaah blessed the sons with guidance to 
    Islam whilst their families remained kaafirs. These scholars did not change 
    their names even though the names were foreign and their people followed 
    kaafir religions. 
When Islam forbade 
    adoption, it also forbade changing the name of the adoptee’s father and 
    tribe. Allaah says (interpretation of the meaning): 
“Call them (adopted 
    sons) by (the names of) their fathers, that is more just with Allaah”
[al-Ahzab 33:5]. 
In a case where the father 
    is not known because the child is a foundling – for example – he should not 
    be attributed to or named after any specific person, rather he should be 
    called as a brother or mawla (freed slave), because Allah says at the end of 
    the verse quoted above:  
“But if you know not 
    their father’s (names, call them) your brothers in Faith and Mawaaleekum 
    (your freed slaves)”
[al-Ahzab 33:5]. 
One of the reprehensible 
    matters in which some Muslims follow the kuffaar is giving the wife her 
    husband’s name. This is haraam. Rather she should keep her father’s name. 
We have discussed the 
    ruling on the wife using a name other than her father’s in the answer to 
    questions no. 2537, 
    1942, 
    4362 and 
    6241. 
Conclusion: 
It is permissible for a 
    Muslim woman to marry a Muslim who has recently converted out of conviction 
    and sincere belief. And it does not matter if his family follow any kaafir 
    religion. The children should be named after their Muslim father and his 
    forebears even if they are kaafirs, and it is not permissible to do 
    otherwise. 
And Allaah knows best.