Professors and the like have been reading emails for long enough that I bet they know these two conventions that you seem to indicate you're unsure of:
- Emails, being not letters, contain who they are from in their
headers. Email readers display this to the recipient in the way in
which the recipient is likely most accustomed to by now.
- Emails may, or may not, have a signature block at the end.
This block is separated from the content by a line of text
consisting of only "-- " (dash dash space). A good email reader
will format, color, or highlight this block differently. A
heavy email user will ignore it.
So right off the bat, you're doing it wrong with how you delimit your signature. Secondly this block should be ignored by the person reading it, unless they're looking for some information they haven't seen in the email or the headers (your address, where, yes, it's okay to repeat your name). Often this is ignored because people once generated them per email with quotes of the day, famous sayings, bible bits etc. thus they're totally about expressing personal tastes. When you assume they're ignored, there's no duplicate information in them to worry about; they're entirely redundant.
When writing formally with an opening and closing as though it were a formal letter, yes, you will say "Dear Your Name" [redundant because the name is in the to header] and "Sincerely My Name" [redundant because your name is in the from header], and in countries like Ireland, Switzerland, Germany etc. where certain signed information is mandatory, there will be a standardized sig block.
My recommendation for your case is to change your signature block a little (if that's permissible) to fix the apparently duplicated lines containing just your name. I'm thinking like:
Dear Prof. Bar,
Please explain how Lagrange multipliers help to find minima of functions.
Address: John Doe at Acme Widget Company
123 Elm Street, Metropolis, ST 00000, USA
At least you're not using one of those totally unenforceable disclaimers that foist some supposed compliant behaviors on the recipient.