It's not like some artist would have sticks / picks printed with their name on if it was deliberately a type of sticks / picks they don't use themselves.
Well, I would, just to put people off if they thought my pick would give them 'my sound'... I'd be like "Hah! You thought that pick would sound more like me, but in fact it sounds less so!" ... but nobody else would be such an 'sshole. 🤗
Or, I suppose some stick / pick firm might send an artist a job-lot of them on spec, hoping the artist would use them and/or give them out to people, which would look like an endorsement... yeah, that could happen.