Changing shape of logo?

To draw a triangle, select your polygon tool, then option+click (if on a mac) or alt+click (if on a PC) somewhere on your artboard. A polygon dialog box should pop up. Enter the number "3" in the "Sides" field area, then click ok. Feel free to use your solid selection arrow tool to drag the triangle edge until it reaches the size you want, or you can hold down shift key while dragging a corner edge if you wish to constrain the shape as it resizes. Now, make your triangle is the top-most object on the artboard. Select the triangle and choose "Object" menu..."Arrange"..."Bring to Front". Now, select the triangle shape and the text, then go to the "Object" menu and select "Envelope Distort"..."Make with top Object".

Jen,

"I've tried this with the logo as a .png and a .eps file."

For a logo, forget about raster formats, and start with vector artwork.

The switch from rectangle to triangle can be made with Envelope Distort using Top Object, but you will dislike the outcome, the crucial word being Distort.

Depending on the desired appearance, you will most likely need to create the new shape (one of) the hard way(s).

Try deselecting everything, and then use the Delete Anchor Point tool on the anchor point you want to delete.

If that doesn't work, can you attach a screenshot with your layers?

It's not entirely clear what your objective is with respect to "a logo," but as for a rectangle that you want changed to a triangle, you'll have to remove an anchor point.

With the rectangle selected, choose the Delete Anchor Point tool (click/hold on the Pen tool; see below) and click an anchor point to delete it. After that, you can use the Direct Selection tool (white arrow) to position the the remaining anchors as desired.