At present, the homepage icon of Twitter is depicting the Doge meme.
The motive behind the modification has not been disclosed by Elon Musk as of now, but users have come up with their own conjectures.

On Monday, Twitter users became bewildered by the alteration of the social media giant’s logo to an image of a Shiba Inu, the dog breed linked with the renowned internet meme, DogeCoin, which was subsequently followed by a meme shared Elon Musk.
Many people are speculating whether the modification of Twitter’s logo to the DogeCoin dog was a prank by Musk or a security breach, which has led to confusion among them.