Is there a way to give a specific file name when saving a file via cURL?

Either use the -o option or its alias --output, or redirect shell output to the file of choice by using >.

curl -o /path/to/local/file http://url.com
curl http://url.com > /path/to/local/file

If you want to preserve the original file name from the remote server, use the -O option or its alias --remote-name.

curl -O http://url.com/file.html 

Stores the output from the remote location in the current directory as file.html.