Praise be to Allah.
With regard to the name Daniyah (دانية), there is nothing wrong with it. The meaning of this name is: one who is close or near, and the intention behind giving this name is optimism that she will be close to goodness, gentleness and easy nature, but it is more like a girl’s name than a boy’s name.
Please see the answer to question no. 116400
With regard to the name Daania (دانيا), it has the same meaning as the name Daniyah, but some people are very keen on names that end with alif, such as Raniya, Randa and Daliya, and with some names that end with ta’, they turn the ta’ into an alif, because that sounds lighter (in Arabic).
However there is nothing wrong with the meaning, as far as we can see, although we do not encourage using this name, because there may be some confusion as to the meaning, and because the way it is written and pronounced is not in accordance with correct Arabic usage.
With regard to the name Daiyaanullah (ديّان الله), the Dayyaan (Judge) is Allah Himself, may He be exalted. Ahmad (15612) narrated that ‘Abdullah ibn Unays said: I heard the Messenger of Allah (blessings and peace of Allah be upon him) say: “The people will be gathered on the Day of Resurrection naked, uncircumcised and destitute.” We said: What does destitute mean? He said: “They will not have anything with them. Then it will be called out to them: ‘I am the Sovereign, I am the Judge (Dayyaan). It is not appropriate for any of the people of Hell to enter Hell when he is still owed something by one of the people of Paradise, until I restore his dues. And it is not appropriate for any of the people of Paradise to enter Paradise when he owes something to one of the people of Hell until I restore his dues.”
Classed as hasan by al-Mundhiri in at-Targheeb wa’t-Tarheeb (4/218); classed as saheeh by al-Albaani in Zilaal al-Jannah (1/266).
With regard to the word Dayyaan, al-Haleemi said: It is taken from the phrase “Maliki Yawn id-Deen (The Only Owner (and the Only Ruling Judge) of the Day of Recompense – al-Faatihah 1:4)”, which refers to the One Who will take account and requite, and will not cause to be wasted the good deeds of anyone.
End quote from Fath al-Baari (13/458)
It also conveys the meaning of the Sovereign Who is obeyed, the Subjugator Who compels people to obey Him, and the Judge.
Al-Bayhaqi (20359) narrated that ‘Umar ibn al-Khattaab (may Allah be pleased with him) said: Woe to the dayyaan (judge) on earth from the Dayyaan (Judge) who is in heaven on the Day they meet Him, except the one who rules with justice and judges in truth, and does not judge on the basis of whims and desires, kinship, hope (of worldly gain) or fear (of people), and He keeps the Book of Allah before him.
Classed as saheeh by al-Albaani in Mukhtasar al-‘Uluw (p. 103)
See also: Lisaan al-‘Arab (13/164)
So calling a child by the name Daiyaanullah is not appropriate, because Allah is the Dayyaan (Judge), and one of the names of Allah cannot be used in conjunction with His name Allah; this is from a linguistic point of view.
With regard to the meaning, the Dayyaan (Judge) is Allah, so no one deserves to bear this name, let alone add this name to His name Allah by saying “Daiyaanullah”.
What the person should do who wants to choose a name is avoid anything that may cause confusion, and not seek out weird names, no matter what his reason is. Rather he should look for good and beautiful names that are familiar in his environment and the meanings of which people know. There are sufficient names that have clear and beautiful meanings, and are easy to pronounce, and there is no need for any of these weird names.
Please see the answer to question no. 1692 for information on names that are haraam or makrooh according to Islamic teaching
Please see the answer to question no. 7180 for information on the etiquette of naming children.
And Allah knows best.