:salam2:
yahya father is zakariyah, in this surah zakariyah duaa is made available to us by Allah, swt.
He wanted so badly to have a son to carry on the family and inherit the noble status that Allah gave them as prophets.
Zakariyah and yahya are the decendants of Jacob, the people of that time new very well the lineage of Zakariyah and new their devote obedience to Allah.
need more information let me know, in sha Allah I will do my best.
here is a different translation than the one you posted, just to give you more understanding:
[
Hilali-Khan] "Who shall inherit me, and inherit (also) the posterity of Ya'qub (Jacob) (inheritance of the religious knowledge and Prophethood, not the wealth, etc.). And make him, my Lord, one with whom You are Well-pleased!".
the greatest thing the prophets wanted was a son to carry on the message of la illaha il Allah.