Five Inches is Standard
According to the luxury goods website Bella Lino, the standard size for letters in bath towel monograms is five inches. The monogram appears centered at the bottom of the towel and rests either four inches above the bottom edge or 1 1/2 inches above the towel's dobby. The etiquette website Gracious Style notes that a standard towel monogram features the first letter of the last name.
It Depends on the Number of Letters
Gracious Style points out that some towel owners prefer to use three letters to represent their first, middle and last names. Some married couples also prefer to monogram each spouse's initials on their respective towels. Because the number of letters in a monogram may vary, and because three five-inch letters may overpower the simplicity of the towel, the etiquette website What Would Jackie Do? suggests that letters in towel monograms may be as small as four inches.
If you prefer just a single letter, go with a 5-inch height. However, three letters of that size would overpower a towel, so stick with 4-inch letters if you opt for monograms with multiple initials.