To control the branding experience on your webpage and get rid of the "Vimeo" logo in the player control, follow these steps.
NOTE: This only works with a Vimeo Plus account.
Log into your Vimeo account. Click on the "Videos" tab.
How to hide the Vimeo logo in the player control
Choose the video for which you want to hide the Vimeo logo. Then click on the Setting button - that symbol that looks like a little Lego wheel.
Click on "Embed" under Video Settings
Scroll down the page until you see a set of checkboxes.
Uncheck the "Vimeo logo" checkbox.
And, don't forget to the click on the "Save Changes" button!
Now, refresh your web page and the Vimeo logo should be gone. If it's still there, make sure that you clicked on "Save Changes" button on the Vimeo page (see step above).