Telford & Wrekin Council has issued the Big Bridge Challenge to schools across the borough.
The challenge will also invite school pupils in STEM subjects to create their own version of the bridge, before it adopts the winning name entry in an official opening ceremony later in the year.
Locals have already unofficially named the bridge "the whale" due to its long curvature and fin-like end.
The council says the new footbridge presents a perfect STEM learning opportunity after it has joint forces with the Year of Engineering celebrations - a national campaign increasing awareness and understanding among young people of what engineers do.
Every pupil that enters the challenge will receive a free pass for Telford Ice Rink, and the best entries will win prizes provided by RAF Cosford Museum and Enginuity Museum.
But Telford Priory School tweeted that the closure of the A442 Eastern Primary in order to lift the bridge this weekend is causing a significant rise in lateness.
The tweet read: "Please note that the A442 is closed both ways until next Tuesday.
"We are experiencing a significant rise in lateness this week. Late detentions would normally be issued for every late arrival without a valid excuse.
"We are being mindful of difficulties during the closure when issuing student late detentions.
"Thank you to those parents who have made the extra effort to get their children into school on time."
The closure is in place so that one of Europe's largest cranes can be built ready to install the main span of the new bridge.
The first of 16 lorries carrying parts of the crane arrived at about 8am yesterday, with more arriving through yesterday and today. The crane is being assembled ahead of the weekend ready for the bridge to be lifted into place in the early hours of Sunday morning.
The bridge will connect Telford Central with Telford Shopping Centre when the work is done. It will be opened to the public later this year.
For more information on how to enter the Big Bridge Challenge, visit telford.gov.uk/footbridge