We have a pretty small team, which makes promoting ourselves to other teams difficult - once you consider the people wee need in the stands scouting, those who are driving, and those we need to keep in the pit to fix the robot and talk to judges, we pretty much don't have anyone left to wander the pits talking to other teams.
So instead, we get ourselves noticed by our actions. We go out and do our best on the field, and focus on working with our alliance partners in every match. We engage everyone else who is going around scouting and stops by our pits. And as others have mentioned here, we've crafted a very distinctive look for our team that stays in people's minds.
We've also noticed that many teams either don't scout or don't know how to do so effectively. Our rookie year, we were in a position to be picking... and our scouting consisted of taking pictures of robots so we could look through them and talk about which robot we thought was best. Fortunately, we had a great team come up to us Friday morning. They said "You're going to be picking this afternoon, and we think we'll be a good alliance partner for you for these reasons... If you're willing to pick us, we'll share this crate of scouting information we've gathered over the past two days." From that, we learned what scouting was and how to actually do it.
So, starting with our second year we've done serious performance-based scouting. Not only that, but we've shared that data with everyone who wants it (and probably with some people who didn't). We print out a summary of our data, showing lists of the top teams in different categories (this year, it would include number of balls scored, number of bridges balanced, stuff like that). We include a cover letter that describes what the data represents and how it was gathered. That then gets delivered to the pits for the younger teams (mostly rookies), and in the past we've had second or third year teams come up and ask for it, remembering it from last year. The goal here is two-fold: We ensure that all the teams picking have good scouting data, which thus far has always helped us, and we ensure that they learn something about how to collect good scouting data so they can do it next year. Plus it ensures that all those teams know who we are
Also, the team discusses scouting Friday night, and pretty much figures out who is going to be on our picking list (if we're in a position to pick), and who we want to watch closely Saturday morning for more information. Teams running around Saturday trying to get noticed don't affect our scouting at all - those in the pits generally have no say on alliance selections. It's the drivers (for feedback on how they work with different teams), and those in the stands who have actually watched every match that make the decisions, and the decisions are based almost entirely on the hard data.