Even if most people in the audience know you, just state your name and give a few words that describe your relationship to the deceased. If it’s a really small crowd, you can start with, “For anybody who doesn’t know me…” If you’re related to the deceased, describe how; if not, say a few words about how and when you met.
Avoid clichés like “We are gathered here today…” and begin as you mean to go on, with something special to that person. After introducing yourself, it may be best to get straight to your point as everyone knows why there are there. For example: “There are many things for which she will be remembered, but what we will never forget is her sense of humour…