Marine here, not historian. A big part of is is the institutional memory of him, rather than any personal memories. Chesty is THE most decorated Marine. In addition, he started out at the bottom, enlisted, then went and became an officer, which gets him a lot of respect, especially when you add his other accomplishments onto it. He really made a name for himself, especially if you look at some of the things he did in the Banana Wars, and obviously later in WW2 and Korea. Maybe not always the brightest, but always the boldest, and that gets you a lot of respect and attention. The USMC is huge on tradition, especially at boot camp, and it gets pushed deep into your head that Chesty Puller is THE Marine, you love him because he's Chesty Puller and that's that. Another thing you'll notice is some of his most famous quotes, he talked like a hard mother fucker (asking about bayonet lugs on a flamethrower? hell yes!) and that's the kind of thing that gets Marine's, especially boots, attention. Look at (now retired) General Mattis for a great example of a Marine who is almost universally loved across the Corps, I'll bet my own money his name is going to live on for a while as well.