Right now, every picture I take are named like this DSC_0237.JPG As a result, When I try to put the pictures in the same folders as other Nikon pictures, the filenames overlap. How to add the date and time in this naming format automatically? Something like: DSC_0237_20180302_131525
There is no option to change the file name in camera. Users can only change the file number sequence method, as @Tetsujin noted. For the record:
In Setup Menu, change File Number Sequence to On. The camera will continuously number images and give them all a unique filename. After 999 images, use the Reset option in File Number Sequence to go back to 001. See the D3100 manual for more details.
Changing the name for each shoot has to be done outside of the camera. The import tool in your digital asset management program will have an option for that. Alternately, use a free-standing app for bulk file renaming.