Have you got something like this in your JCL?
//FILE1 DD DSN=date.dataset.one,DISP=SHR
// DD DSN=date.dataset.two,DISP=SHR
As far as I know, there is no useful way to tell which dataset a particular record came from. If "one" is empty, your first read will get the data from "two" and will then get EOF passed to you when "two" is read (the second time your filename is read in the Cobol program).
The solution for the above JCL is to count how many reads are successful. If there are zero, one or more than two records, abend. If there are exactly two, you have to "hope" they come from different datasets.
"Hoping" isn't much good in computing.
So, make them seperate DD names in the JCL. Checking file-status and processing EOF for your files, count the records as you read them. If there are zero or more than one records, abend, for each of the two date files in the program.
Read through all of the above postings to be aware of some of the issues and resolutions. Bear in mind we had no idea you were talking about "concatenation". Next time, please be more clear.