Pipe grep to copy files based on name.

[Daffy]

I just finished restoring some files from a friend's hard disk. All files are now into a folder and I need to transfer some of them.

While it's easy to copy files with a certain extension, I cannot understand how I can copy them using the filenames.

To select files to copy based on the extension, I just use cp *.(extension) /destination/folder/.

To list items based in name, I used

ls | grep name\ to\ search

I think that it will be something like

cp | grep name\ to\ search

but where do I specify the destination folder?

How do I pipe grep to cp to transfer files based on name?