How to enable identify the music option in Cortana?

Huh, weird. Before going and performing a hard reset, let me take a quick look through the settings and seeing what I can find.

EDIT: Don't see any options for it. Might be a backend server issue (Cortana relies HEAVILY on the cloud, so many problems can be traced back to server issues), which means a hard reset might not help. Go for it if you want, however.
 
Actually I hated reset again yesterday and I had the option again but now it's gone again.

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Just try asking her instead. Ask her "What song is it?" and she will listen to it and give you the result.