The orchids in your photos are all dendrobiums. It is a good practice to cut off the flower spike after the blooms have fallen off of the plant. It appears, at least in the last photo, that the actual plant has been cut off mid-stem. This is not a good practice. If those parts of the plant are dead, they can be removed at the base, but cutting them in the middle can expose the plant to infections if any green is left in them.
The stems that have been cut will not bloom again. Some dendrobiums will actually put out another flower spike on an older growth -usually next to a previous spike as is seen in your first and second photos. Most likely, your dendrobium will produce a new growth and will spike and bloom from that growth.
To rebloom your dendrobiums follow the care instructions below from the RVO Orchid Care Page:
2000 - 2500 footcandles
Very easy to grow, Dendrobiums enjoy abundant light and bloom profusely.
70 - 90 degrees F. daytime, 60 - 65 degrees F. night.
40 - 65 % relative humidity is ideal
Dendrobiums can grow quite tall with flower sprays reaching 3 - 4 feet in length budding out near the crown. Nobile types require a cool rest period in winter to initiate budding but bloom all along the length of the cane.