Rail-to-rail is often a marketing term. Given a supply of 0V-15V I'm not sure that you can actually get down to 0V on the output for 0V on the input. There simply must be some voltage drop across the output driver. Given that the supply voltage is higher than the required output (15V supply, 10V signal) there should be no problem on the top end.
Well, that's true. Output swing also depends on the output current. Also, RtR can mean RtR input, or RtR output, or both. Probably, no need for full RtR input here, but common mode should include V-.
Sadly, I don't have any part numbers at hand, but there are devices from, e.g., AD, that designed for near-negative-rail output.
Also, a rail splitter (e.g. TLE2426) can be an option. I think I saw circuit where an unused opamp was used for it, but can't find the schematic.
UP: also a charge pump can be a solution. Like lm7705 or I even saw just a two-lead device that is to be inserted into opamp's negative rail. But I forgot the part number

. Although, these are more exotic solutions, availability and cost of rare parts often a no-go. But for one-off project why not?
