Christianity proclaims to man the commandment to love one's neighbor. Prayer for our relatives and friends is a clear confirmation of our feelings for others. It is possible to make commemorations for all people, but it is in the Church that they pray only for her children - those who have been baptized. However, Orthodoxy does not interfere with prayers for those who have not been honored with the great sacrament.
There are several types of prayers. For example, church (commemoration during worship in the temple) and cell (prayer at home). You can also distinguish between prayers for health and repose, supplication, thanksgiving and repentance. There is congregational prayer, when several people come together to make requests to God, and along with it there is also a private prayer. For all baptized people, the Church allows you to pray in the church, and for the rest, a person must turn with requests to God at home.
In the Christian tradition, it is impossible to commemorate the unbaptized in the church because these people are not members of the Church. But they cannot be left without prayer. Any requests for a person can be uttered at home in front of the icons. Here you can use both general prayers from the prayer book (for health, repose, or others), and use your own words. The Lord looks not just at stereotyped texts, but looks into human hearts and souls. Each petition for any person should be from the depths of the heart.
You can also pray for dead unbaptized people in the Church, but you cannot order a commemoration. Nobody forbids praying in your own words. You can also do this at home. There are even special canons in prayer books for such cases. There is a practice of praying to the martyr Uaru for those who did not receive the sacrament.
You can read the psalter in memory of both the deceased and the living. And, of course, if a person himself is a believer, he can ask the Lord not only for help to his neighbor, but also for the Lord to grant a loved one or a friend a person to accept the sacrament of baptism.
Some prayer books contain special petitions for unbaptized people. There are many such prayers, so everyone who wishes can, if they wish, turn to God. It is enough just to buy such a book in the church and boldly perform the feat of love for one's neighbor, determined by prayer for him.