The name of Allah al-Haqq (The Truth) means The One Who’s existence is true and The One Who does not change.
This is similar to our general usage of the word “truth”. When we say that something is true, we mean it actually exists. We say, for instance, that 2+2=4 📝 is true since this rule actually exists or that 2+2=10 is not true since such a rule does not exist. We say that a police report 📄 is true if it describes what actually happened (or existed in the past) and false otherwise. And so on.
Furthermore, the truth, unlike falsehood, does not change. Events that took place, rules in science 🔭 and math, etc do not change. Part of being true is consistency.
So the name al-Haqq (The Truth) has a meaning similar to our general usage of the term “truth”. But how exactly should we understand this name when it comes to God?
al-Haqq is The One Who’s existence is True
God’s existence is true and does not depend on anyone or anything. It is unthinkable to imagine that God will cease to exist at some point or that He did not exist at some point before we were created. That’s simply because His existence does not rely on another being (in which case He wouldn’t be God in the first place).
The existence of everything else, including our own 👪, is dependent on God. The only reason we exist is because God chose to create us. Therefore, our existence (while it is still true from one aspect because God created us) is not “ultimately true”, since our existence is dependent and not intrinsically from ourselves.
al-Haqq is The One Who does not change
As mentioned above, one of the meanings of truth is consistency. When it comes to God it means that God does not change in His existence, names, etc.
In particular, God is The Merciful and will continue to be so since He does not change. He is The Knowledgeable and His knowledge does not change. He is The Wise and His wisdom stays the same. And so on.