Set<String> otherProgramsValueSet = new Set<String>();
    for (Lead em : Trigger.new) {
if(em.Email != null){
    listEmail.add(em.Email);
}
if(em.What_is_your_primary_program_of_interest__c != null ){
    listname.add(em.What_is_your_primary_program_of_interest__c);
}
if(em.Other_Programs__c != null){
// this will construct a set of values selected in multiselect. Set will maintain unique values.
// Multiselect values are semi-colon separated, hence the split function.
    otherProgramsValueSet.addAll(em.Other_Programs__c .split(';'));
}
}

//Query account records with matching names.
//Iterate over this list to create new Affiliation records
 List<hed__Affiliation__c> affiliationListToBeInserted = new
 List<hed__Affiliation__c>();
 for(Account acc : [select id from account where name in : otherProgramsValueSet]){
affiliationListToBeInserted.add(new hed__Affiliation__c(Account__c= acc.Id));
}
insert affiliationListToBeInserted;