Looks like it was Dick Grayson who gave Damian Wayne permission to assume the Nightwing alias.
From – Injustice Gods Among Us Year 5 #14
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I can’t believe it. Not for a second. As Deadman, Dick HAD to be able to see what Damian was doing, that he was killing as part of the Regime.
True. Or possibly Dick hoped that by taking on the Nightwing mantle, Damian would see the error of his ways. Dick’s always been a bleeding heart.