The names that CPLEX generates for cuts are always of the form
<character><number>
where <character> is a single character and <number> is a decimal number. So, if you use a different naming pattern (for example two characters instead of one) there should be no name clashes. Or are you saying that CPLEX generates two cuts of the same name?
Note that cuts and constraints are in different namespaces, so in general a cut and a constraint may have the same name. If you read out a cut from CPLEX and then add it as a regular constraint then you need to change the name of the cut to avoid name clashes. In this case the safest thing to do is to always rename a cut before adding it as a constraint -- or to not use names at all if that is possible.
#CPLEXOptimizers#DecisionOptimization