TL:DR; There's no way to set your profile picture specifically for Ethos.
Ethos uses your profile picture from Twitter if attested, ENS if you're not attested, or blockies if you have neither ENS or Twitter.
Ethos currently depends on other connected services for your profile picture. The default profile picture used for a wallet is your blockie, or an automated image that is associated with your address that you might be used to seeing in Metamask or other wallets.
Otherwise, we set your profile picture based on
If you have an ENS registered for that wallet and have set your profile picture there, you'll see that profile picture used on Ethos, unless:
If you have attested x.com/Twitter, we'll override your ENS or blockie with your current profile picture there.