First of all, if you only have the name and no reference to the constraint, then you have find back a reference to the constraint. This can be done by using an IloIterator and checking the name of each constraint. This is not very efficient, so if possible store a reference to the constraint, not its name.
Next, there are no facilities to deactivate a constraint. What you could do is to clear its left-hand side or set the right-hand side to infinity so that the constraint becomes redundant. Both are not recommended unless absolutely necessary.
Is there a particular reason you cannot remove/add the constraint?
#CPLEXOptimizers#DecisionOptimization