Do people see my losses in Dota 2?

By default people can't see your losses.

However if you have enabled Share Match History in options,people will be able to see your losses(and even more stats) on the online sites like dotabuff by searching for your name(no matter if friends or not).

Nobody but you can see the number of your losses or abandoned games in your in-game profile and there is no way to change it.

By the way, since July 26, 2013 wins and level are also hidden from non-friends by default:

Wins and level are now hidden for players that aren't friends and don't have 'Share Match History' in the options enabled

However, as Arremer reminds us, with enabled Match History, third-party websites can show many different statistics. For example, DotaBuff shows your win/loss ratio and the number of games that you played while "Share Match History" was enabled.