I'm not sure what the conventional first words of a Pope are, but the traditional announcement of a new Pope goes like this:
Annuntio vobis gaudium magnum: Habemus Papam, eminentissimum ac reverendissimum Dominum, Dominum Georgium Marium Sanctæ Romanæ Ecclesiæ Cardinalem Bergoglio, qui sibi nomen imposuit Franciscum.
I announce a great joy to all of you: we have a Pope, the most eminent and reverend lord, Lord Jorge Mario Bergoglio, Cardinal of the Holy Roman Church, who took for himself the name Francis.
Note that some Popes use the accusative and some use the genitive for the name at the end of the announcement; Francis chose the accusative.
If you want to use this phrasing, you would say mihi nomen impono Thomae (or accusative Thoman/Thomam): "I take for myself the name [of] Thomas".
EDIT: As brianpck points out, the accusative is Thoman in Greek and in earlier Latin, but Thomam in later Latin.