As Orthodox Christians, are we permitted to have memorial services in our church for those relatives who are not Orthodox? What about adding names of non Orthodox Christians to our lists for Saturday of the Souls, etc.
Since becoming Orthodox, I have found so many of the practices and sacraments to be such a fulfillment and comfort. I realize that is my duty to pray for all people—Orthodox or not—in my daily life, but there is also something very comforting about hearing the names read during Liturgy, or a memorial.
There are a few possible answers to your question.
There are those Orthodox who feel that it is proper to pray for anyone and everyone, whether they be Orthodox or not, both in private as well as public.
There are those Orthodox who feel that, with regard to services other than the Divine Liturgy, it is proper to pray for non-Orthodox but that in the commemorations during the Divine Liturgy only Orthodox Christians should be remembered in prayer.
There are those Orthodox who feel that under no circumstance is it proper to pray for anyone who is not of the Orthodox faith. This, of course, is somewhat odd since in the Divine Liturgy we pray for the catechumens, that is, for those who are preparing to be baptized into the faith but who are not yet members of the Church. There are a number of other practices and examples which would tend to contradict this understanding.
With regard to the practice at your local parish, I would suggest that you seek the guidance of your pastor in this regard.