This discussion will be seem clearer afer examining the final code offered--which is very short. But to gain some knowledge and understanding, which is always importnat...
The read command works by using the characters stored in the IFS variable -- "internal field separator", by default whitespace -- to separate out the tokens/fields on each line it reads, and then loads the variables specified at its arguments, one token per variable. But if any tokens remain, they are all added to the last variable specified. So when you say read oldname newname, 2 variables are specified. The first parsed token is loaded into oldname, and the remainder of the tokens into newname. I.e., the first filename is being loaded into the var oldname, but newname is getting extra stuff besides the 2nd filename (the carriage return, or anything else after the second filename). (MS uses '\r\n' --CR/LF--to end lines, Unix just '\n' (i.e., LF)). So then one might think the following would work, which has a "garbage collecting" third variable for read:

Code:

#!/bin/sh
while read -r oldname newname trash; do
cp /path/$oldname /path/$newname
done < /path/to/textfile.txt

The previous code works only if there is some whitespace after the destination (2nd) filename on each line of the file. If so, the '\r' and the filename will be separated by whitesapce, and since $IFS is whitespace, read will treat the '\r' as a separate, third token, and it will be loaded into our trash variable.
If there is no space after the 2nd filename, the second token will be "dest_file\r", in which case you first have to get rid of the carriage returns (if you don't, the 2nd argument to your cp command will be meesed up). The filter tr -d '\015' will remove a carriage return. (015 is the octal ASCII code for carriage return, and tr -d deletes the specified character).
Even so, you may still may want to use a third "garbage collecting" variable, in case you have any comments in the file, which would mess up your cp command. E.g.

Code:

old_checkbook.dat  new_checkbook.dat  ' my checkbook data

Just make sure there are no spaces in the filenames you have. Otherwise, hopefully you have used a non-whitespace to delimit the source filename form the target filename. (If so, script will need to be fancier.)
Also, if the filenames in the file are from an MS machine, and you want to put the files on a Unix box, make sure the directory delimiter is '/', not MS '\'. You can do that with the filter tr '\' '/'
So in the end, we end up with this, whi h is basically just a more robust version of Perderabo's code:

Code:

#!/bin/sh
tr -d '\015' < /path/to/textfile.txt | tr '\' '/' | while read -r oldname newname trash
do
   cp "/path/$oldname" "/path/$newname"
done