To the IL grandchildren I am grandmommy. My oldest GS would call me grandpapamommy so I got him to say just grandmommy and that has stuck with the 2 for almost 19 years.
To the AR grandchildren I am grandme(username now) Oldest GS here would call his grandfather pepe but finally got it to grandpe. The 2 little ones chose grandme after hearing the older ones call me that. They call their other grandmother grandma.