Does prolonging supplication after the final Tashahhud by mentioning worldly matters or names of people invalidate the prayer?

Prolonging supplication (Du'a) and mentioning a specific need therein after the Tashahhud of the last unit (rak'ah) does not invalidate the prayer. This is because this is a moment when supplications are answered. It was narrated from Abu Umamah (may Allah be pleased with him) that the Prophet (peace and blessings of Allah be upon him) said: "Which supplication is most heard?" He said: "In the last part of the night, and after the prescribed prayers." "After the prescribed prayers" refers to their end, after the final Tashahhud and before the Tasleem (salutation of peace), as Ibn al-Qayyim preferred, arguing: "The 'end' (dubur) of everything is part of it, like the 'end' (dubur) of an animal." It is also authentically reported in the Sahihayn and other collections, from Ibn Mas'ud (may Allah be pleased with him), that the Prophet (peace and blessings of Allah be upon him) said: "Then let him choose whatever supplication he likes best, and supplicate."