French has only one word where English has two. Baptiser means to admit or initiate someone into the Christian Church by baptism and to give them a name in the course of the ceremony of baptism.
It can also be used in a figurative way as a synonym of appeler, nommer/surnommer and applied not only to people but to objects too. It is exactly the same in English with the verb “to christen”, here is part of the definition of “to christen” in the OED:

To name, give a name to; often with complement, to call by the name of. colloq.

So just think of baptiser as “to christen”. The part of the sentence you don’t understand could be rephrased thus:

un bracelet en caoutchouc qu’elle a appelé « Nous prions pour le Japon »