rental income - tax implications

My wife and i have recently bought an apartment and it has just been let through an agent.
The agents have sent me a letting agreement in my name only.

As my wife only works a few days a month - i imagine it will be more advantageous to have the rental income spilt for tax purposes. ie her half would be taxed at the lower rate.
Am i right in this assumption and should I ask the agents to put the letting agreement in both our names (or does this make any difference)

Thanks in advance

Your assumption is correct.

No need to have lease amended as property is in joint names.

Best of luck