Formation of partnership firm

one of our client want to form a partnership firm in the name and style of say  ''ABC'' . Now the name '' ABC Private Limited '' is already there . 

Question : 

1. Since exacly same name is there, can we form the partmentship firm in the same name as above held by Private ,limited co.  ? 

2.  If we do not register the firm and form unregistered with same name as mentioned above , is it allowed ? 

3. If we register the firm with the same name as above , is it allowed ?