I know the King of Morocco Mohammad V chose to do this relatively recently, in 1957. These questions could also extend to other countries in North Africa and the Gulf States.
Was their anything culturally or practically notable about adopting the title King rather than Dey, Bey or Sultan?
Was their internal government reasonings behind this, or did the king himself personally choose this?
Was their a reaction domestically?
Traditionally, Muslim leaders avoided the word "king" (Malik) and reserved that title for God (it's one of the traditional mystical "99 names of God"). However, in the mid-20th century, this began to change. The Hashemites declared themselves Kings of Arabs in 1918 (by 1924, this was reduced to merely being King of the Hejaz), with the Saudis conquering them and taking the title in 1927 (changing it to King of Saudi Arabia in 1932). The first Hashemite King's eldest sons ended up as King of Iraq in 1921 (after failing to become King of Syria in 1920) and Emir of Jordan (after declining to become King of Iraq in favor of his older brother). At independence in 1946, the Emir of Jordan became the King of Jordan.
The Egyptian Emir was the first to follow the Hashemite lead, declaring himself King of Egypt in 1922 (briefly becoming the King of Egypt and Sudan before losing power). The King of Morocco is another. The process is still going on. In 2002, the Emir of Bahrain became the King of Bahrain.
In general, the way I've understood it is that Hashemite adopted their title in WW1 as an explicit way to claim suzerainty over all of the Arab people (at least in Arabia, Mesopotamia, and Greater Syria). Think Lawrence of Arabia, and so also think this could also betray some English or at least general European influence, though I haven't read anything explicitly making that case. The rapid collapse of the Ottoman Empire allowed them to do this. Their regional rivals, starting with Egypt, wanted to engage with them on equal terms with equal titles so quickly switched styles as well. Later, other Arab houses also switching creating a sort of new norm that replaced the previous norm of avoid the title "King". As for internal reactions to these title changes, I honestly don't know of anything. A few Arab monarchies retain alternative titles. The United Arab Emirates famously (they are unlikely to change soon as their organization is based on the theory that they're seven equal federated states, a title change by one of the Emirates like Abu Dhabi or Dubai could affect that formation). The Sultan of Oman is another holdout, though it's worth noting that Oman is not a Sunni majority state or Sunni ruling house, so other norms may be in play (I unfortunately know little about Oman other than it's rad).