I want to know if Muslims can attend the Naming Ceremony of a New Born Baby, whose parents did not have Nikah and can we eat the Meat Slaughter for the baby, if no, how is such baby given a name and other Islamic rites for the baby

All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger.

It is not permissible to attend the ceremony which you mentioned for two reasons:

1) Participating in the celebration of a new-born baby whose parents are fornicators is confirming and being pleased with their sin; rather, it is an obligation to deny what they did and call them to repent to Allaah. Celebrating the baby who is born out of fornication and making this public is publicizing that great sin and exposing the shamefull act. On the contrary, we are religiously obliged to desert the dissolute people who sin openly, and not participate in their celebration.  

2) Celebrating the naming of the new-born child is not permissible in Islam, as it is not legislated in Islam to celebrate the naming of the new-born child whether or not the new-born is legitimate. Rather, it is the 'Aqeeqah which is legislated and naming him on the seventh day. Therefore, celebrating the naming of the child is an innovation in religion.

As regards naming the child born out of fornication or adultery, then he should be named like any other child but he is not to be traced back to the fornicator (father from fornication or adultery), rather, he is traced back to his mother and she should choose a good name for him. However, according to the view of some jurists it is desirable for the mother of a child born out of fornication or adultery to offer an 'Aqeeqah for him. This is the view we adopt here in Islamweb, but this does not necessarily mean she openly does it and expose the shamefull act; this view implies that the hair of the child should also be shaved on the seventh day and its weight should be donated in charity (in silver).

For more benefit, please refer to Fataawa 97254 and 81160.