Is it permissible to verbalize the intention when paying Zakat by saying, "O Allah, this money is the Zakat of my wealth," and if not, then how should the intention be made?

The place of the intention (niyyah) is the heart, and it is not legislated to utter it aloud in acts of worship such as prayer, fasting, and zakat. Uttering the intention aloud has only been reported in two instances: when entering into the state of ihram for rituals, such as saying "Labbayk Umrah" (Here I am, O Allah, for 'Umrah), and when slaughtering a sacrificial animal (hady), an Eid sacrifice (udhiyah), or an 'aqiqah, by saying "Bismillah 'an fulan" (In the name of Allah, on behalf of so-and-so).

Therefore, whoever wishes to pay the zakat on their wealth should intend it with their heart, without uttering the intention aloud.