Change ID string in vcf file with awk

I have a VCF file with SNP IDs like this:

AX-14233402__rs35404821
AX-37499887__rs74704183
AX-36783275__rs11997571

I would like to change the SNP IDs to have only the IDs without the AX-... term:

rs35404821 
rs74704183 
rs74704183

Is there any solution for this? I tried with a gsub command, but nothing changed:

awk '{gsub(/AX*_rs/,"rs"); print}' datafile.vcf > datafile_ID.vcf

>Solution :

With your shown samples, please try following solution. What this code does is: Setting __ as a field separator for all the lines, then checking condition if line starts from AX- then printing 2nd field of that line.

awk -F'__' '/^AX-/{print $2}' Input_file

OR in case you want to simply print values after __ without checking if line starts from AX- or not then try following.

awk -F'__' '{print $2}'  Input_file