Associating between results obtained after running Trinity's run_DE_analysis.pl and genes

Question

[langziv]

Hi.
How can one associate between the generic transcript names and the actual genes of the studied organism? Here are the first few lines of the output file kallisto.gene.counts.matrix.Control_vs_Serum.edgeR.DE_results (which I understood is the relevant one for differential expression analysis):

sampleA sampleB logFC   logCPM  PValue  FDR
TRINITY_DN20_c32_g3     Control Serum   9.23276616667445        12.9356943987126        2.99593148556322e-21    1.20271669487936e-16
TRINITY_DN4_c16_g1      Control Serum   8.63278061282675        10.5525746902278        2.83205795956004e-18    5.68464833932689e-14
TRINITY_DN16_c15_g4     Control Serum   8.1299403156539 12.8442074535907        1.08780718396644e-17    1.32166860920557e-13

I looked at the other output files but didn't find a relevant information.
I got the organism's fasta file of annotated CDSs. Should I use it in blastn to annotate the differential expression results?