Does read sequence identifier need to be unique for proper alignment?
What tool did you use to replace the read names? Can you modify that to split up the reads into separate files or encode the cell barcode in the read description instead of the read name? 

Typically is it assumed by many tools that the FASTQ read names are unique. you could have issues with BWA and split alignments but I don't know if that pertains to your data.  I think the best you can do is the sanity check the results at each step of the process.

In the fastq format (https://en.wikipedia.org/wiki/FASTQ_format) on the first line denoted by the '@' there can be two values separated by a space.  The first is the name and the second is the description.  

So an example would be:

@Original_read_name CGAGGCTG_TATCCTCT_AGTCCA
ATCGATCATGATGACA
+
@&amp;%*@(%@%*($!##!