🚀 go-pugleaf

First, I assume that the Illustrator eps or ai file has had its 
lettering converted to vector outlines; otherwise just selecting the 
text for editing would reveal the font name.

Many logos are either created with unique lettering or use an existing 
font, graphically enhanced, distorted, or otherwise modified.

There are a couple of tools that are sometimes useful -

http://www.whatthefont.com
and
http://www.identifont.com

WhatTheFont takes an image (limited to 200K pixels and disconnected 
letters in a straight line) and analyzes it. If the font (or 
equivalent) is sold by MyFonts, it can often identify it correctly. 
Otherwise, its result can be unpredictable.

Identifont asks a series of questions, which you can limit to the 
characters you actually have. Again, sometimes it hits the nail on the 
head and sometimes not.

There are also forums, including this one, where there are 
knowledgeable people who can help you identify a font if you provide a 
link to an image.

Others include typophile.com and usenet newsgroups comp.fonts and 
alt.binaries.fonts (in the binaries group you can post an image directly).

  - Herb