Variable: completion-base-size

Number of chars before point not involved in completion.
This is a local variable in the completion list buffer.
It refers to the chars in the minibuffer if completing in the
minibuffer, or in `completion-reference-buffer' otherwise.
Only characters in the field at point are included.

If nil, Emacs determines which part of the tail end of the
buffer's text is involved in completion by comparing the text directly.