Single Initial vs. Monogram

When people ask me to personalize any kind of accessory for either themselves or for a gift, they often ask if it's okay to put just the last name or first name initial vs. a full monogram.  While there is no right or wrong answer to that question, I tend to suggest that a monogram be used instead of a single initial when possible.

My reasoning for this is straight from the definition of personalize. 

Personalize: (verb) To mark something in a way that shows it belongs to a particular person.

That being said, there are also occasions when a single initial does just the trick.  These two darling girls made their first day of school dresses one of a kind just for them!