batch - Copy list of files to new names

Windows 7 Pro

I want to copy a series of files, all named "cover" from different directories to a single directory, and give them all new names. I need help with either of the below options:

Option 1
Use a batch file to copy the source files to a single directory as "cover1", "cover2", etc., then rename by hand.

I can use the below one-line batch file, but it copies files sequentially to the name "cover" in the directory "A", resulting in just one final file.

for /f "delims=" %%L in (Coverscopy.txt) do copy "%%L" A

I presume I should use a loop to add a number to the filename, but I'm afraid I don't seem to know how to vary the file name with each cycle.

Second option
Use a batch filed that draws from a CSV file with columns for the original file address and the desired new name.

Unfortunately, I have no idea where to start with this.

Any assistance appreciated.