Monogram traditonally means the use of one initial letter to represent an entire name - used as first or last initial, first and last initials, or first, last, and middle initials.
The first initial of a persons first or last name can be used for a one character monogram.
The first and last initial can be used side by side embroidered in the same size for a two character monogram.

For a three letter monogram the persons first, middle and last names are used. As an example let's use Susan Valerie Jackson. All three letters can be the same size where the order is first, middle, then last initial. SVJ
Another choice might be to have the last initial in the middle and larger than the first and middle initial, S J V
Another choice would be to embroider his towel with his initials and her towel with her initials.

Monograms for the traditional couple:
For example George and Susan Jackson could be monogrammed with the first initial of the groom on the left, the first initial of the bride on the right, and the last initial in the center in a larger font.
Using just their last initial J as a sinlge character monogram is also a popular choice.

For the modern couple using a hyphenated name: As an example let's use George Jackson and Susan Carpenter. The first initials would flank the last names as above, except there'd be 2 last name initials. G JC S

If both the bride and groom have hyphenated names, an acceptable 4 character monogram may be applied.
Thomas Frank Olsen-Wright and Karen Marie Smith-Jones could have the first initials of each first name flanking the first initial of each ones last name.
TOSK (Thomas Olsen Smith Karen)
Another option would be to keep it simple and use just a single letter monogram of each of their first names.