I have read in the chain of many Ahadith that some narrators are named 'Israel.' I know that Israel is the name of Prophet Jacob, but is it ok nowadays to name our children 'Israel?' Is it also ok to name them Mikhaeel or Mikael, as the angel?

Praise be to Allah, the Lord of the Worlds; and may His blessings and peace be upon our Prophet Muhammad and upon all his Family and Companions.

There is no harm in naming children with the names of Prophets and angels because there is no evidence prohibiting that.

This is considered among the general good names which the Hadith ordered us to name the children after the names of prophets.  The Hadith states: "On the Day of Judgement you will be called by your names and the names of your fathers, so make your names good." [Reported by Ahmad and Ibn Hibban]

Ibn al-Qayyim said in his book ‘Tuhfathul Mawdud’ that 'The chain of narrations of this Hadith is good,' and so said al-Sakhawi in his book ‘Al-Maqassid’.

However, in the chain of narrations of this Hadith there are some interruptions that’s why Shikh Albani and Arnout said that it was a weak Hadith.

The other evidence about the permissibility of the above (naming after Prophets and angels) is that our righteous predecessors used to name after the names of Prophets and angels.

Bukhari and Muslim wrote a chapter about naming after the names of Prophets, and they both mentioned the Prophet (Sallallahu Alaihi wa Sallam) naming his son Ibrahim (Abraham).

They also both mentioned that the Prophet (Sallallahu Alaihi wa Sallam) said: "Name yourselves after my name."

In the Hadith of Ahmad, Ibn Dawud, and Nasa’e (it is reported): "Name yourselves after the names of Prophets."

Ibn al-Qayim stated in Tuhfat-ul-Mawdud when mentioning that it is permissible to name after the names of Prophets, that Talha (Radiya Allahu Anhu) had ten children and he gave them (all) names of Prophets (Alaihim Salaam).

Al-Dhahabi stated in Siyr A’lam Al-Nubala, that many predecessors named themselves with the name of Jibril and Mikael.

Allah knows best.