#Python 2, 42 19 16 Bytes
Python 2, 42 19 16 Bytes
lambda n:n[1:-1]
Try it online! Thanks to @Kritixi Lithos for saving 23 bytes! Thanks @math_junkie for saving 3 more bytes. For input, put each part of the name as a string within a list like so:
["Samantha", "Vee", "Hills"]
And yes, the OP has approved a list to be a valid input.
Explanation
lambda n:n[1:-1] # Returns only the middle elements... pretty literal here