I would think Franz Liszt's surname would be pronounced "least" or "leasht," but according to this, it is pronounced "list." Is that true? If so, why?
The name is pronounced as the German word "List" which comes very close to the English word "list".
To understand it, you have to know that Franz Liszt was an Austrian-Hungarian composer. In Hungarian his name is Liszt Ferenc. In Hungarian "sz" is pronounced similarly as the German "ß", and in fact in former times the modern German letter "ß" was written as "sz". And up to now in "ß" is pronounced as "s - z" ("ess- tsett") when one pronounces the individual letters.
His father was Adam Liszt whose name is also spelled as Adam List which is of German origin. His professional career took place in the Kingdom of Hungary (see Wikipedia) which was part of the Austrian empire. In Hungarian the letter "s" is pronounced as the English "sh", and this explains the spelling with "sz": Adam Liszt wanted his name to be pronounced reasonably correctly.
Yes, true. It's a name. It's pronounced as the person who bears it wants to see it pronounced.
Further, it follows the usual way a 'i' is pronounced in German when followed by a consonant: short like the 'i' in the English 'list'. The sz is a rare and antique way to denote the ß character when the ß is not available - but the ß actually is a ligature letter for the combination sz - either way, it is pronounced as the 's' in the English 'list', too.