More detail about this can be found here:
http://www.quakeworld.nu/forum/viewtopic.php?id=3539

Simply put, this would be an in-game modification of the scr_teaminfo in
place of the console or overrides the console and reduces it to 1 line of
text when active.

When the team-match starts, the HUD_TeamTalk display is divided into as many
separate lines as there are teammates and each line is reserved solely for
that teammate. To signal a new message being sent from a teammate a quick
flash colored overlay could be highlighted over the visual console members
line of text. For instance:

Team1-Reppie: Get Pent
Team1-Milton: Need RL
Team1-You: Got YA

This will organize team messages and will prevent the need to spam the same
message repeatedly to get your message appropriately noticed. Spam can also
be further reduced if the last message sent is always onscreen until
replaced by a new message.