the and adjective

I have seen that some people prefer to use “the” with certain adjectives. For example

  1. the great source of motivation instead of a great source of motivation (I used “a” here because apart from that person, there can be other sources of motivation)

  2. The preferred choice instead of a preferred choice

  3. The big name instead of a big name

  4. The name you can reckon with instead of a name

Is it mandatory to use the in some cases so that the subject can be highlighted?

You don’t need the adjective. ‘The’ is used with that noun to represent the fact that this stands out as distinct from its competitors.
The adjective is used for the same purpose which is why they are often paired together.
It’s certainly not mandatory.