As-salaamu 3laikum, I heard the name Lawgiver being used to refer to Allah but is this one of His names and are His laws one of His attributes? Or is that only if the law is revealed in Allah's words in the Qur'an but not if it is revealed in another way like through a hadith? Jazaakumu Allahu khair

All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger.

The name lawgiver (or Musharri') is not one of the Names of Allaah, The Almighty. It is known that the Names of Allaah are determined by revelation (the Quran and Sunnah), so there is no room for human reasoning or personal judgment. Thus, Allaah is not named except as He has named Himself in his Book, or as the Prophet has named Him in his Sunnah, and it is neither mentioned in the Book of Allaah nor in the Sunnah of His Prophet that Allaah is named the lawgiver.

However, it is said that Allaah is the lawgiver as a declarative statement - in other words, to inform that He is the one who makes laws - but not as one of His Good Names. To make laws is a F'iliyyah attribute of Allaah, i.e. an attribute that is related to His actions; just as He has control over all created things, sends the winds and sends down the rain, He makes whatever law for His slaves that He wills.

Sheikh 'Alawi ibn 'Abdul Qaadir As-Saqqaaf said: "Legislating is a F'iliyyah Attribute of Allaah, The Almighty, which is confirmed in the Quran and the Sunnah. It is a feature of His Lordship, and whoever challenges Him in it, then he has indeed disbelieved. Allaah is 'The Legislator' and He is 'The Lawgiver' but these are not from His Names. The evidence about this in the Book of Allaah is the verse (which means): {He has legislated for you of religion what He enjoined upon Noah and that which We have revealed to you, [O Muhammad]…}[Quran 42:13]. The evidence from the Sunnah is the Hadeeth by Abdullaah ibn Mas’ood who said: “Whoever would like to meet Allaah tomorrow as a Muslim, then let him preserve these prayers wherever they are called, for indeed Allaah legislated for your Prophet the Sunan of guidance, and they are indeed from the Sunan of guidance…” [Muslim] Indeed, the scholars, in their statements, often attribute legislation to Allaah Almighty...” [Abridged from his book "The Attributes of Allaah the Almighty that are mentioned in the Quran and the Sunnah"]

The fact that legislation is an Attribute of Allaah does not mean that the laws are limited to the Quran apart from the Sunnah; rather, laws are taken from the Sunnah in the same manner that they are taken from the Quran, because the Prophet  delivered the message from Allaah. Whatever the Prophet has legislated, it is in fact a legislation from Allaah. For this reason, the Prophet informed us that there will come people who would consider the Quran as the only source of legislation and reject whatever the Sunnah has legislated. He said: “It will be very soon that a man from you will belie me while leaning on his couch as my Hadeeth is narrated to him. He will say 'Between us and you is the Book of Allaah, and whatever lawful thing we find in it, we will deem it lawful, and whatever unlawful thing we find in it, we will deem it unlawful'. Verily what the Messenger of Allaah forbids is like what Allaah forbids.” [Ahmad, At-Tirmithi, Ibn Maajah and others]

To forbid is also a part of legislating; As-Sindi said in his commentary on Ibn Majah: “What the Messenger of Allaah has forbidden is exactly what Allaah has forbidden, as the act of forbidding is attributed to the Messenger on the strength of him delivering the message (of Allaah), but it is actually Allaah who has done so. What is meant is that [what the Messenger has forbidden] is the same in terms of the obligation of being obeyed and the necessity of being acted upon.”

Allaah Knows best.