I had the same type of problem in FTM2012, but have not seen it in FTM2014 yet; although my mini-tree, at the top of the Person tab becomes "detached" from the "selected person" often in FTM2014 and has never happened in any previous version.
My experience was a tad different, in that in my situation, the names sorted by surname fine, but new names for the first name would sort to the bottom of the surname, first name combination and be out of date order.
Have you tried clicking on the header where it shows "Name"? My experience was that that a time-consuming procedure for me (for 60,000 plus names) and only lasted that work session. Since you only have 3,000 name, the time shouldn't take that long.
Also note the you can click on the down arrow at the top of the Index screen, or the top of the person tab and it will list all the people you have worked on in that session.
And, finally, you can always navigate to the Tree tab, find your person there, then return to the Person tab - very inconvenient.
I would report this as a bug at:http://ancestry.qualtrics.com/SE/?SID=SV_er4cyPjj5BJKIZf
or email to:firstname.lastname@example.org