Non-religious funerals
You are free to organise whatever kind of funeral you wish.
Many people these days are not religious, so it may feel strange and awkward, and out of character, to give a non-religious person a religious funeral. That said, religions are geared up to perform the rites of passage, and so have time-honoured rituals that are designed to bring comfort to the bereaved.
It is perfectly possible to hold non-religious funerals, but they need careful organization and creative effort to substitute the religious ritual. Essentially, mourners like to be confident that the event will take place smoothly and with appropriate solemnity.
The British Humanist Association offers guidance on how to organise a religion-free funeral, and can provide people ('celebrants') who will officiate; see www.humanism.org.uk