If I understand your question correctly (and to quote the words you use):
You are "actually looking for the most proper way to write the sentence [you] used as an example", namely:
Names starting with "earlier" letters come first in lists.
Personally, I would rewrite that as:
Names are listed alphabetically.
Names are listed in alphabetic order.
If you want to retain a similar format to your example:
Names starting with letters earlier in the alphabet ...
Names starting with alphabetically earlier letters ...
Names higher up the alphabet ...
but personally, I'm not keen of any of those alternatives.
More importantly, in referring to "Names starting with ... letters ...", you could be understood as implying that only the first letter is taken into consideration in determining the order, such that you could have a sequence such as:
Howe, Holmes, Hancock, Hill, Hughes
whereas true alphabetical order would take into account all letters in the name (as far a necessary) to give:
Hancock, Hill, Holmes, Howe, Hughes