Looking for suggestions on how to trim this opening.

I'd leave that one the way it is.

yep agree with joe.....no reason to trim that ..it blends in just fine...

Those are arch ways rather than doors and would normally not be trimmed, unless they are in a period home. The only way to trim the narrow one is to reduce its width approximately 8-inches by constructing a 4-inch wide section of wall on both the left and right side. With these narrow sections of wall protruding from the existing walls which are now flush archway, you would be able to install normal jamb and casing.

An 8-inch reduction in width would appear to make the doorway too narrow based on your photo, so best to leave both of them 'as is'.

Whatever they are called, they are non-doored openings between rooms or areas. I think the frame in the first example would look weird because it only has 2 sides. The second example could be framed - we have a fairly modern house with a framed opening into a room from a hall and it looks fine. One thing that I try to do is remain consistent in the theme of a house (style, trim, etc.), so if the two openings are in the same general area of the house, if you're not going to frame the first one I wouldn't frame the second.

Thank you all for your inputs. I'm going to leave them alone