Hi there - you're right a name first, then the badge. A few for consideration, I'm totally not married to any of these..but it might get some better creative juices going...
Garnet Babes garnet is January birthstone...although a Jan BFP would mean September-ish due date....so,,,
Snowflakes (I think this was used?)
Snow Owls (They are known to aggressively defend their nests and will attack those that disturb their nests :)).