What is the ruling regarding someone who discovers that he is the son of Zina (illegitimate, born out of wedlock) and was attributed to someone other than his biological father, and what are the resulting Sharia issues, such as the ruling on shaking hands with the son of his mother's maternal uncle, what should he do when getting married, and the ruling on using a pseudonym to avoid the forbidden name?

You are obligated to be dutiful to your mother and maintain ties with your siblings, while concealing your mother's situation and not revealing her secret. When you marry, one of your brothers should act as your guardian (wali) for the marriage contract. As for your mother's maternal uncle's sons, they are non-mahram (definition) to you unless there was fosterage (رضاعة), and you must veil from them and avoid shaking their hands if possible. However, your mother's maternal uncle (khal) is a mahram to you. You are not required to change your name which is attributed to your mother's maternal uncle if that would lead to scandal. It is preferable to use a pseudonym in your work, while being careful not to participate in activities that involve forbidden matters.