Add row from table B based on minimum distance between table A and B

I am a beginner with PostgreSQL and have two tables A and B, both with multiple columns, including a point column (geom): TableA includes a given 'ID', geom, etc , TableB is a "DB" of locations with a 'name' column, geom, etc... **Need to find for each TableA.id what is the the 'name' (row columns) and distance of the closest location in TableB.** already could calculate the distance between all points of TableA and TableB with : ST_DistanceSpheroid(pointA,pointB,[SPHEROID]) But the best could build so far, is a select query where provides for each TAbleA.ID all distances and respective names from TableB - does not find the minimum for each ID only. **While needed to have the new calculated columns (distance and name) added to Table A.** It is not yet clear to me how to work with data output when using "select" vs an actual table data output. or use of views.