The LT 65 does in fact have a name as well. She is "portsmouth lady" the LT 66 (which is her sister ship and no longer in the navy) was named Kittery Queen.

Many thank's for your efforts to identify this one guys, renamed it LT 65 and moved to Auxiliaries category. :-)

BRGDS / foggy

Almost not a mystery ship now. The picture could be named LT 65. Thank you Mister Schneider.

The two Army-design 45 Footers at Portsmouth have been with the Navy at least since 1965, possibly since they were new. The Shipyard calls them LT 65 and LT 66 (For "Little Tug," not to be confused with the Army designation). LT 65 is officially C5840 and LT 66 is officially C5841. Both were part of a contract for Army tugs administered by the Navy, but I have never been able to connect the several that ended up in Navy service with their Army origins.

I found a picture on a scale models forum of this ship or a very similar one with the number 66 on the funnel. The picture was clearly taken at the same spot, same brick building on the background and the ship moored at the same barge.
I also found a picture of 45WB0801 at http://www.boothbayregister.com/article/shipyard-working-portsmouth-naval-shipyard-tugboat/59954
and it is not this mystery ship.

There were (are) three tugs in the PNSY tug service YTB-771, YTL-602 and 45WB0801. So it could be the last one as some of 45' tugs were reclassified as Work Boats by the US Navy. But the number 65 on it is a mystery to me.

The only thing I can add it's a (former) 45' ST type Army tug and the number on it has something to do with the pennant number. But I think you already know that.

Sorry that's correct. YTL-602 was the one on the other
photo to the right.

Doesn't match YTL 602:
http://www.navsource.org/archives/14/10602.htm
https://tugster.files.wordpress.com/2010/07/0aaaap6.jpg

It's a YTL 422-class small harbor tug.
Could be YTL 602 since many years in use at the Portsmouth Navy Yard. Built by Robert Jacob, City Isl. N.Y. 10-45.

I found some other pictures of this small tug, but no info whatsoever. It can be seen at the left of http://www.shipspotting.com/gallery/photo.php?lid=1470462#. The two other tugs present are identified, Keokuk (YTb-771) and Cocheco (YTL-602) but not a word about the small one.