There are many ways to create a text logo in Illustrator. One way is to use the Type Tool and create a text style. You can then use the Text Options dialog box to customize the text. Another way is to use the Draw Text tool and create a text outline.
PRO TIP: When creating a text logo in Illustrator, be sure to create it at a high resolution. Otherwise, the text will appear fuzzy and unclear.
You can then fill in the text with the appropriate typeface and font size. A final way is to use the Glyphs panel and create custom glyphs for your text.