The Greek word ἔχωm, echo, Strong 2192, means simply 'to have' and is thus translated on six hundred and seven, out of about six hundred and thirty, occasions of its use in the KJV, according to Robert Young.
The Greek word here used, κατέχω, katecho, (kata + echo), Strong 2722, occurs nineteen times in the KJV and is variously translated but always in the sense of 'hold fast', 'possesss' or 'retain'.
I have noticed elsewhere that there is sometimes a tendency to translate the 'kata' element of Greek words somewhat simplistically, as a mere physical downward force, and I suggest that this has been done with this word, giving it a meaning of 'hold down' leading to the idea of 'suppressing' truth or 'hiding' truth, or 'keeping truth to oneself'.
In the context, Paul is speaking of hypocrisy throughout chapters one and two of Romans and I suggest that hypocrisy is the essence of the 'possessive holding' of 'truth', to which the apostle, here, draws attention.
Kata is often used in matters of headship or regarding authority, in relation to that which is under the 'downward force' of the headship or power. Here, also, I would suggest, the emphasis is on a possessive regard to that which is truth. It is the deliberate action of commandeering 'truth' as though it was under one's authority ; as though one had some custodianship of truth itself.
Paul uses the article in 1:18 'the truth' yet he has not mentioned truth before so I would say it is not the anaphoric article (referring back to a previous mention of concept) but the absolute article - 'that which is truth'.
Thus he is not focusing, say, on the gospel as such, nor even on the revelation to Israel, I suggest. It is all truth, it is whatever is true. Truth itself.
Yet to do so, when the righteousness of God is not satisfied (in regard to oneself) is sheer hypocrisy. Paul has mentioned the righteousness of God at the beginning of the epistle and made it clear that the wrath of God is revealed from heaven against all ungodliness of men on earth.
He will speak of it again, later in chapter three, but here he brings all humanity to account and here, in 1:18, he deals with those who would lay claim to 'truth' as though it was theirs and as though they had possession of it.
But they do so in unrighteousness. They are not right in God's sight. The righteousness of God is not at rest in regard to them.
'Holding' truth'; 'possessing' truth'; being 'custodians' of truth : is an utterly hypocritical irrelevance, if a man be not just in the sight of God.
Later, in chapter three, Paul will deal with how, exactly, 'man shall be just with God' (as Job says). But here, before one gets to that point, one must examine oneself and determine what is one's relationship to God above, as revealed by one's deeds and words, rather than determined by one's hypocritical possessiveness about what must be, essentially, a sheer theoretical distraction, if one is still an unrighteous person.