Baby Name Poll

Patrick Alexander Schaffer is the name we decided on for our son. My grandpa recently became very ill and has been diagnosed with cancer. Everyone in my family feels we should include his name into the baby’s name some how. Grandpas name is Eugene but he goes by Gene. I really don’t like that name for a guy especially with the G. His initials would be PAGS which I don’t like... Would it be weird if I spelled Gene either JENE or JEAN for a boy? Jean spelled this way is actually my, my sister, my mother, and my grandmothers middle names...I would much prefer his initials be PAJS if I have to have 2 middle names. What should I do? I don’t want to hurt my family. Any ideas? Thanks for your time. By they way I will NOT use Eugene...my grandpa can’t even stand his own name he has always gone by Gene.