Yes, check trademark and also website domains.. Avoid confusion and misbooking.
But at the end of the day however pretty and marketable a name, it has to connect to the land you are working or it makes no sense to me. Look at named landmarks/woods/rivers on your land that aren't already in use as farm names locally.
What I don't get is if you have a farm, surely it already has a name..
Should be on your RPID or IACS or whatever farm registrations go under, at least if it's agriculturally registered. Even if it's "part something else" where a farm has been split, you can look at compass/map and call it East X or whatever the relevant direction, or Lesser X if it's a tiny part you've taken off a large farm, or look at local naming traditions and fit in to those. Here you'll get Easter and Wester X rather than East and West, the original farm is X Mains or Mains of X. If it doesn't have a holding number and farm ID already then you'll need one..