Quotation marks will work if it is mainly just one character.
If more than one character, you could have the names for the first instance they talk, followed by first initial thereafter. (Just a suggestion.)
For example:
Dave: "I wish I could fly."
Steve: "You are not a bird so you can't fly."
D: "Bats fly, and they're not birds."
S: "Don't get technical with me, Boyo."
I submitted a ms in this format and, while the ms didn't sell, there were no negative comments (or comments at all) about this format.
Best of luck!