Your avatar needs to remain identifiable when it appears next to a short reply or a fast moving conversation. A photograph of several people or a detailed business card is usually difficult to recognise there. Choose one face or a compact mark and remove unnecessary scenery through the crop. Keep the identity simple enough that it still works without its accompanying account name.
X's profile help recommends 400×400 pixels for profile images. This page selects that square export. The uploaded image is still displayed at different sizes across the interface, so compare it small rather than judging it only in an enlarged preview.
Leave breathing room around the head or symbol. A square file can be presented with a rounded mask, making content in the corners unreliable. If the source contains a wide wordmark, use a compact brand variant instead of forcing every letter into a tiny profile image. The crop cannot redesign the mark for you.