You have to get down to the bare glass and there's a clear coating that you have to strip as well then you can do a rough polish but you will want to terminate the end and polish with a puck and polishing paper against a very flat hard surface such as a mirror.
This looks like bare fiber but it's not, there is still a coating that will burn when the laser is powered up.
Here it is after the coating has burned back some, but you want to strip it off then hand polish, terminate and finish polish.
In your pic you still have the coating on the glass, you need to strip it off then polish the glass fiber without the coating or it will foul the surface, the polished face of your fiber is an optical component and needs to be clear. I can see a problem in the center, also you need to strip off the coating.
I have used this, first use the fine then the extra fine, polish in a figure 8 motion keeping the puck flat with light pressure, you will need to get a termination and the puck separately, what fiber coupled module do you have, look it up and find the dia. of your fiber then search ebay for a termination and polishing puck.
--edit-- Ok I see you said SMA so find a SMA terminal, if you want to you can hand polish your fiber but you have to strip it down to the bare glass and use the diamond film paper.
Once you have a SMA termination glued in and polished you can look for a collimation lens, something liket this >
https://www.ebay.com/itm/Thorlabs-F...239661&hash=item41f3a63dc6:g:rb4AAOSwcWJb7IEs
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