If you ask the people that have self identified it then yes. It is where the Tenderloin meets Nob Hill. So it isn't Nob Hill but it isn't the Tenderloin either.
There are many "neighborhoods" like that in the City. Another example is the area now called NOPA for North of the Panhandle. Over the past ten years they have organized to the point where they are involved in all aspects of neighborhood life from safety to econominc development. Another example is the Middle Polk neighborhood where the same things have happened.
Yes it is above trendy loin, and below Nob Hill. Trendy names for neighborhoods, such as tender nob, reflect a clear perception of micro neighborhood differences, that you won't find on any map.
No, it's not as far as realtors are concerned. The official SF Association of Realtors' title for this neighborhood is "Downtown" and its the area bordered by California St to the north, O'Farrell St to the south, Polk St to the west and Stockton and Market to the east.
I don't know of any official reference to it as a neighborhood but a lot of people refer to the areas where Nob Hill and the Tenderloin meet as the Tendernob. Some also call it Lower Nob or Upper Tenderloin.
I've actually noticed this area evolve and become a safer and hipper area with lots of trendy bars.
I was recently at a roof top bar (very NY-esque) called Jones in the Tender Nob. Right around the corner were two very swanky bars, Bourbon and Branch and Tradition. Highly recommend all three, just be safe and don't take your phone out when it's not necessary as there is a lot of iPhone theft around there.
In my mind and many others it is a neighborhood that the community are very proud of, and what makes a neighborhood than people :-) At some point in the future as others have had happen it will be officially recognized.
Of course it is! I've been a regular patron of businesses in the area and it was always referred to as the Tender Nob by shop owners and neighbors alike. They used the term affectionately and with no hesitation.