Yes, you can put "The rest of the evening" at that start of the sentence.
A normal sentence is in active voice. Here is an example:
I spent the evening at home.
You can turn it into a passive voice sentence by removing the subject and moving the object to the front:
The evening was spent at home.
In a passive voice sentence, the active-voice subject is called the agent and the active-voice object is called the patient. In the above sentence, the agent is missing and the patient is "The evening".
You can add the agent, but if you need an agent, you should think hard about whether you should be using passive voice at all.
The evening was spent at home by me.
Passive voice is useful when we don't know who the agent is, or it's not important to specify, or if the really important part is the patient. You can read more about passive voice here.