To Analyse the words grammatically - verbs, nouns, singular, plurals, past tense etc.
Look at the words linguistically
What does the dictionary say about a word?
What is the root of a word?
What are the related words?
What meaning do we get?
What are other meanings of a word? e.g. Deen = religion, action, recompense, judgement
To study the words contextually - what does a word mean in the context, sentence, circumstance, environment.
The word. ٱلرَّحۡمَـٰنِ A'rahman, Mercy
Grammatically, the root words are
ر ح م - r h m
ٱل Al = the
Rahman = Mercy. Is the word a noun, a verb, is it singular or plural etc.
Linguistically - what the dictionary says about the word – the root stems from the mother's womb, from that we get other words such as love, tenderness, pity, forgiveness, vulnerability one of the words that branch out is mercy - Rahman
Contextually - how the word relates to the rest of the sentence. Allah is merciful to all. We get feelings of encouragement when we say Most Merciful, Especially Mercifully, because of Allah's mercy and compassion.
This is the pattern to follow when doing word analysis.
So the actual word we are studying remains the same it does not change we are just looking at the deeper meaning, what the original root word is so you get a deeper understanding.