Haha, using the first name IS embarrassing in their culture (if what we read from manga and anime is real).
It's like admitting that the two of you have an intimate relationship for everyone to hear.
@Lyanhyrt apparently it's not just a trope, it's apparently very common to use last name in Jap culture. Some exchange students came to my Uni back then from Japan and they addressed me with my last name when they had questions.
For those that don't get the whole first name thing, instead of first names, imagine they are calling each other darling, honey, or sweetie. That's almost how it feels for them.