The general term for changing tube and pipe diameter is swaging. The tools you are looking for exist but vary widely in price and complexity. It may be more straightforward to find a local metal supplier who can do the swaging for you based on your specifications.
Flaring vs. Swaging
I am unsure if there is a specific name for the process which is the opposite of flaring, however flaring is not quite what you are looking for. The term flaring is generally applied to the process of making the end of a tube or pipe or tube a conical shape of larger diameter than the original tube or pipe, especially for special plumbing fittings called flare fittings and is shown below. The image shown is from the link provided. The flared end of a copper tube is shown at the marker (C) in the image, while the nut marked (B) goes over the left-hand threads on the male fitting, sealing the connection.
The general term for continuously deforming hollow cylinders by mechanical action to change their diameters is swaging (Wikipedia). Swaging is similar to drawing and extrusion. Drawing and extrusion are terms generally applied to solid, constant-cross-section bodies such as rods, while swaging is generally applied to tube and pipe. Additionally, the swaging process is usually applied only to a portion of the length of a tube or pipe for some engineered purpose, as you are seeking.
A diagram demonstrating the process of swaging, which is done by drawing or pressing a tube or pipe through a die, is shown below. The pipe is moving from the left side to the right side of the image, through the yellow-colored die, and its outside diameter is being decreased as a result. The image is from www.felss.com.
Benchtop swaging equipment does exist, such as at this link from www.mscdirect.com , though depending on what you want to do the price may vary and end up significantly lower, such as at this link from www.directindustry.com. No affiliation or endorsements are implied with these links and they are intended for illustrative purposes only.
Another option is to find a local metal part supplier who has all of the tools and order the pieces custom-made to your specifications. The materials and labor to shape the materials will probably end up being less expensive and higher quality than with a novice DIY approach if this is a one-off or proof-of-concept. Additionally, you have experts who know how to cold work metal and may be able to provide minor additional advice.