Mr Hawkins said while the dental school did not go for "Craney", "Reachie" fitted that theme.
The name had nothing to do with Leighs Construction's being founded in Christchurch and Mr Hawkins said most staff who worked in Dunedin supported the Highlanders.
Being Otago-born, McCaw also had links to Dunedin.
"We wouldn't want the crane name to have anything to do with the Crusaders.
"We don't want to come in and find it burnt down," he joked.
The crane would not keep the name Reachie McClaw as Leighs Cockram JV gave it a different name each time it was put up.
A University of Otago spokeswoman said the crane, which was so tall two other cranes were required to assemble it, towered over the 37m-high Forsyth Barr Stadium, but it was edged out by the 56.3m-high First Church spire.
The crane, from Smith Crane and Construction in Christchurch, was assembled in sections before being hoisted into position.
The Walsh Building, beside the construction site, was closed as a precaution over the weekend.
The crane will be used in the construction of the School of Dentistry's $125 million clinical services building, which is due to be completed by September next year.