Message on the Thank you gift

In a few weeks, it will be my father’s death anniversary (one year since he’s passed). Many relatives and friends will be coming to the ceremony. My mother has bought small gifts to give to them as a thank you. What is the name of this gift? I’d like to know what should be written on the message that is put on the gift wrap. Should the name of the deceased loved one be written? The dates of birth and death? Is there any other message? Should there be any images? Are there specifics to this kind of message?

Is this supposed to be done in accordance with the traditional Japanese custom, i mean, is this going to be in Japan?

If so, I assume you are talking about the white “wrap” or cover paper with the gray or black & white “ribbon” printed across, which goes over the box of the gift you give to the relatives and friends who have come to the occasion. You would write 志 above the printed ribbon lines, and the family name (in kanji, vertically) below the lines.

Is this what you mean?
Something like this?
https://houji.haijin.co.jp/香典返しの掛け紙・表書き/

Actually, a lot of Japanese people including my family don't write anything on those gifts. Moreover, a 香典返し is something you give in return for a 香典, so if you're not receiving 香典 for some reason (such as your rituals not following Buddhism or declining money the way many modern people would), the message would not fit.

The people at the ceremonial hall would know better. If not, it just may not be that kind of a ceremony, which is wonderful in its own way.

You can write a simple message on the gift wrap like "In Loving Memory of [Father's Name] (Year of Birth - Year of Passing)." You can add a brief note of appreciation, such as "Thank you for joining us in remembering [Father's Name]. Your support means a lot to us."