Mentioning husband’s or wife’s name in front of people
Question

                In many cultures a person is refered to as father of so and so or mother of so and so.  Also generally women do not call their husband by name but refer to them as father of their eldest child's name.  Is there evidence in the quran and sunnah for such a thing and if not, how do this practice start? 
Is it islamically wrong for a woman to call her husband by his name or for a man to call his wife by her name when mentioning him/her?
Praise be to Allah.Firstly: 
Yes, it was proven that some of the Sahaabiyaat (female Sahaabah) mentioned their husband by their kunyahs (“father of So and so”). Examples of that include the following. 
It was narrated that ‘Awn Abu Juhayfah said: The Prophet (peace and blessings of Allaah be upon him) established the bond of brotherhood between Salman and Abu’l-Dardaa’. Salmaan went to visit Abu’l-Dardaa’ and he saw Umm al-Dardaa’ looking unkempt. He said to her, “What is the matter with you?” She said, “Your brother Abu’l-Dardaa’ has no interest in this world.” Then Abu’l-Dardaa’ came (to visit Salmaan) and he made food for him, but he said, “I am fasting.” He said, “I will not eat until you eat.” So he ate. When night came, Abu’l-Dardaa’ went to stand in prayer. [Salmaan] said to him, “Go to sleep.” He slept a while, then he went to stand in prayer. [Salmaan] said to him, “Go to sleep.” When the end of the night came, Salmaan said to him, “Now get up.” They prayed, then Salmaan said “Your Lord has rights over you, your own self has rights over you and your family has rights over you. Give each one who has rights over you his rights.” [Abu’l-Dardaa’] came to the Prophet (peace and blessings of Allaah be upon him)  and told him about that, and the Prophet (peace and blessings of Allaah be upon him)  said, “Salmaan spoke the truth.”
(Narrated by al-Bukhaari, 1832) 
It was narrated that Faatimah bint Qays said: My husband Abu ‘Amr ibn Hafs ibn al-Mugheerah ‘Ayyaash ibn Rabee’ah sent word to me, divorcing me, and he sent with it five wasa’ of dates and five wasa’ of barley. I said, “Do I have no maintenance apart from this, and should I not spend my ‘iddah in your house?” He said, “No.” I got dressed and went to the Messenger of Allaah (peace and blessings of Allaah be upon him) . He said, “How many times has he divorced you (talaaq)?” I said, “Three.” He said, “He was right when he said that he does not have to spend on your maintenance.”
(Narrated by Muslim, 2721) 
 Secondly: 
With regard to a woman mentioning her husband by name, there is nothing wrong with that. For example: 
It was narrated that Zaynab, the wife of ‘Abd-Allaah (i.e., ibn Mas’ood) said: I was in the mosque and I saw the Prophet (peace and blessings of Allaah be upon him). He said, “Give in charity, even if it is from your jewellery.” Zaynab used to spend on ‘Abd-Allaah and on the orphans under her care. She said to ‘Abd-Allaah, “Ask the Messenger of Allaah (peace and blessings of Allaah be upon him) whether it is enough charity for me to spend on you and on the orphans under my care.” He said, “You go and ask the Messenger of Allaah (peace and blessings of Allaah be upon him).” So she went to the Prophet (peace and blessings of Allaah be upon him) and found a woman from among the Ansaar at the door, with a similar question. [Zaynab said:] Bilaal passed by us and we said, “Ask the Prophet (peace and blessings of Allaah be upon him) whether it is charity enough for me to spend on my husband and the orphans under my care. But do not tell him who we are.” He went in and asked him. (The Prophet (peace and blessings of Allaah be upon him)) asked, “Who is it?” He said, “Zaynab”. He asked, “Which Zaynab?” He said, “The wife of ‘Abd-Allaah.” (The Prophet (peace and blessings of Allaah be upon him)) said, “Yes, she will have two rewards, the reward of upholding the ties of kinship and the reward of charity.”
(Narrated by al-Bukhaari, 1373; Muslim, 1667) 
It was narrated that Khuwaylah bint Maalik ibn Tha’labah said: “My husband Aws ibn al-Saamit divorced me by zihaar [saying “you are to me as my mother’s back”], so I came and complained to the Messenger of Allaah (peace and blessings of Allaah be upon him). The Messenger of Allaah (peace and blessings of Allaah be upon him) argued with me on his behalf and said, “Fear Allaah, for he is your cousin (son of your paternal uncle).” I did not leave before Allaah revealed the words (interpretation of the meaning): 
‘Indeed Allaah has heard the statement of her (Khawlah bint Tha‘labah) that disputes with you (O Muhammad) concerning her husband (Aus bin As‑Saamit),’
[al-Mujaadilah 58:1]
(Narrated by Abu Dawood, 1893; classed as saheeh by Ibn Hibbaan and al-Haakim. See Khalaasat al-Badr al-Muneer, 2/229) 
Thirdly: 
With regard to saying one’s husband’s or wife’s name in front of other people, that depends on local custom (‘urf) of the people in any given society. In some societies, doing that is disliked, and in some societies it may even be seen as a lack of gheerah (protective jealousy). In the hadeeth of Ibn Mas’ood mentioned above, Bilaal (may Allaah be pleased with him) mentioned the wife of Ibn Mas’ood by name (Zaynab). If a woman is well known by her name and it is OK for people other than her husband to mention her by name, then how about her husband? 
It is preferable to mention people by their kunyah rather than their names in some societies, or in front of some people. Many problems arise from taking the matter of mentioning people’s names lightly. 
And Allaah is the Source of strength.