Yes Deepak, Liquid variables and expressions work in the subject line as well as the body. So something like this in the subject field is perfectly valid:
New Contractor Request for {{ attribute.ne_first_name }} {{ attribute.ne_last_name }}
To make sure you are using the right variable reference, open your notification under Admin > Templates > Notifications and look at the attribute references shown in the editor. If you want to pull a value from the request being submitted, you could copy it from the Method column under Request Attributes. If you want a value from the existing profile instead, the ID Code column under Your Attributes would be the one to use. This keeps you from having to guess the exact attribute UID.
The Preview button only shows formatting and styling. It will not resolve the variables, so they will show up as raw {{ }} tags. To confirm everything populates correctly, it would be best to test through an actual workflow execution.
If you want to explore more of what Liquid can do in NERM (filters, conditions, loops, nested objects), Zack’s KB post on Liquid Template language use in NERM is a great reference.