The way you 'put someone down as' can show your personal judgment or opinion about them. He is often put down as arrogant because he's very confident.
Pro Tip 2/3
Avoid Assumptions
Be careful to have evidence before 'putting someone down as' something; it could be harmful to their reputation. Without proof, you shouldn’t put her down as a thief.
Pro Tip 3/3
Cultural Sensitivity
In some cultures, 'putting down as' could be considered offensive if done without consideration. He felt offended when put down as 'just a clerk'.