The best place to find personalized coolers is often at a local gift shop that does monogramming and sells all types of blank totes, stationery, etc. But we've rounded up a few online sources...
The monograms aren't visible on all these images, but we made sure each of these can be personalized with names or initials. Another good web search is to look for sites that sell bridesmaid and groomsmen gifts.
The cooler above is L.L. Bean's Softpack Cooler, $25.
Related: Picnicware: The Wine Quiver