I made a banner ITH for my GDs first birthday - she'll turn 6 in May - and used my then largest hoop, which was 240x200 mm or about 8"x10". I did her name, one letter at a time using an alphabet here on CuteEmbroidery and one with the number one on it between the name (Ruth) and the Dutch word for years. Have made a new number each year as a badge with a buttonhole. Thanks for reminding me I'll have to do the 6 and maybe 7 and 8 as well.
I hope this can help. When I make a banner, I stitch out one letter and then decide what size to cut my triangle. This way I can leave a seam allowance to hem and have my letter centered. Then, I use that as my pattern for the rest. I hope it makes sense.