In lesson 1.1 the word shénme sounds different to me when used in the lines asking for the surname and first name. Is there a reason for this?

I just took a listen and you are justified in pointing this out because they aren't exactly the same. First, let's consider that Chinese is tonal unlike English and thus doesn't inflect the voice like English in order to ask questions, etc. The key point is LIKE ENGLISH. What I mean is that Chinese does raise the voice at the end for questions and whatnot but Chinese does it differently than English; Chinese must still incorporate tones also! I recommend not to think about this too much but rather keep listening to lots of Chinese and you will get a feel for it. That being said, What you heard in the first shenme was more of an obivous questioning tone applied to a word that obviously isn't going to be confused tonally for another word. The second shenme is placed in the middle of a sentence where the 'me' syllable in shenme is always neutral tone.