How is al-dahr related to Allah in terms of names and attributes?

Al-Dahr is not one of Allah’s Names.

The hadith, “Allah says, “I am al-Dahr (time),”[1] was narrated from Abu Hurayrah who said: The Messenger of Allah (ﷺ)  said: “Allah, may He be glorified and exalted, says: ‘The son of Adam inveighs against Me, he inveighs against [the vicissitudes of] Time (al-Dahr), and I am Time, in My hand are all affairs, I alternate the night and the day.”

This hadith does not indicate that al-Dahr is one of the names of Allah, rather what the hadith means is that Allah is the One who controls time.

Al-Khattabi said, “What this means is: I am the Owner of Time, the Controller of all affairs that they attribute to time, so whoever inveighs against time because it does these things, is in effect inveighing against his Lord Who is the One who does them.”

Al-Nawawi said, “What is meant by saying ‘Allah is al-Dahr (Time)’ is that He is the One Who causes things to happen, the Creator of all things that exist. And Allah knows best.”

Shaykh Ibn ‘Uthaymeen (may Allah have mercy on him) said, “Al-Dahr is not one of the names of Allah, and whoever claims that is erring for two reasons:

1. His Names are the most perfect and beautiful, they should refer to the most eloquent and beautiful meanings. Hence we do not find any name among the names of Allah that does not refer to any attribute. Al-Dahr is such a word, and it cannot mean anything other than time.
2. The context of the hadith renders that impossible, because He says, “I alternate the night and the day”; night and day are time, so how can the thing that is controlled be the one that controls them?”[2] [3]

References: 

[1] Al-Bukhari (4826) and Muslim (2246)

[2] Fatawa Shaykh Ibn ‘Uthaymeen (1/163)

[3] http://islamqa.info/en/26977