I believe I have an answer for you about the manufacturer.
There is a circle around the character, which is common in Japanese for use in brand names, logos, indicating special meanings, and so on. In this usage circle is "maru" so I searched for 丸新 (Marushin) and found this company (#14 of the last section, same information as below).
新留木刀製作所 Niidome ...
Your tracing isn't quite right: the bokken has a short down stroke at the top of the left character. The correct kanji is shown below, is pronounced "shin" or "arata", and means "new" in English.
Unfortunately, it's such a ubiquitous kanji that I haven't been able to narrow search matches down to anything useful.
Thanks to @Sardathrion I was able to "deduce" the correct answer.
It is indeed Tachi Nage (as you can see here, for example: https://www.youtube.com/watch?v=QRaylht6NNo) where Suga Sensei is performing a series of techniques while wearing a stheated sword in his Obi.
Alternatively also "SAYA NO UCHI" is a general term for this (saya means "Scabbard" - see ...
The closes I can think of is "tachi dori" although that is a set of techniques within the goshin no kata against bokuto, not with. Apart from that, I do not think there is a specific name to those. After all, they are just application of normal techniques.
Touching the spine when the sword is raised is basic kihon waza. It insures alignment and helps practice the full arc and art of kokyu. We were always encouraged to do so to feel the effortless swing and affects of gravity that is halted by the lower body, not entirely by the arms. It is basic form. For true swordsmanship one would not strike this way as one ...