Any there any low end portable recorders, that are capable of naming files by scene and take # (instead of just "00001"}? I haven't used them but I'm talking about gear like the H6, Tascam DR-680, rolad R-44.

The Tascam DR-680 cannot.

"Any low end portable recorders, that are capable of naming files by scene and take #"
- Not easily AFAIK. The Tascam 680 offers three user name presets but limits it to six prepended characters, and the top-panel access made it difficult and time-consuming to access, (and near impossible in a run n' gun bag). Though the new firmware now makes it possible to reset the take numbers w/o re-initializing the entire machine.
The F8 looks better/easier with front panel access and 'history' of folder/file names, but no cigar in it's current state, as far as I'm aware.
I'm not familiar with other Zoom or Roland machines

Take a look at the Tascam HD-P2. Documentation Product: HD-P2 | TASCAM (http://tascam.com/product/hd-p2/downloads/)
"By default the HD-P2 names new projects, files, and markers using PROJ, TAKE, and MARK name pre- fixes. You can change these four letter defaults in the System and Project Settings menus. Projects, files, and markers can be renamed at any point using the built-in renaming screen."