My name came up on the C10 roster without my going to the promotion board. Does that mean that I'm promotable now?

Go, did you even ask your NCOs before coming on here? Come see me with your 2 quart after breakfast lol

Yes, sounds like you are fine as long as you are not flagged and have recently passed the APFT. According to cut off score rules and train the promote rules you should see your name populate on the by name list by the end of this month eff: 1 March 2018. The 20th is the key day of the year for publication of the promotion list. If I understood all of the circumstances correctly this is solid, however please check with you S-1 section for confirmation. Good luck and congrats!

This is part of the Command List Integration. Basically you have hit the mark in the Army where you are eligible for promotion, have not yet been to the board, and have be put on this list. Being put onto the list does give you 39 points, and if your MOS skill level 2 points hit 39 you should be promoted. If you had been denied command list integration you would have been counseled, and barred from continued service. Denying the Command list integration requires a reason from your chain of command, that can be backed up by counseling.

Read up on it, so you know what you're being subjected to. And then Do as SFC Jason Boyd said and go talk to your first line.

http://www.armyreenlistment.com/cli.html