How can one disavow their current lineage if they do not know whether they are an abandoned child or a child of fornication, especially given that the person to whom they are attributed has passed away?

You bear no burden for what your parents did, as Allah Almighty says: "That no bearer of burdens will bear the burden of another, And that there is not for man except that for which he strives." (Quran 53:38-39). You are not sinful for being attributed to that man before you knew the truth. However, now that you know, you must cease attributing yourself to him, as Allah Almighty says: "Call them by [the names of] their fathers; it is more just in the sight of Allah." (Quran 33:5). And as the Prophet (peace be upon him) said: "Whoever knowingly attributes himself to other than his father, Paradise is forbidden for him." You should attribute yourself as Abdullah or Abdul Rahman. If there are Sharia courts, present the matter to them to obtain the necessary documents.