What is the technical name for a lens which has the same maximum aperture throughout the entire zoom range?
This is a constant maximum aperture zoom lens. The "maximum" is often omitted — "constant-aperture zoom" — but is useful to include the word maximum to resolve a possible ambiguity with a fixed aperture lens, which is a much more rare design where there is no ability to stop down the lens from its one and only aperture setting.
Fixed aperture is only common in catadioptric lenses, which use mirrors, and I'm not aware of any that zoom, so in some sense the distinction is pedantic; everyone will know what you mean if you say just "constant-aperture". You will find people calling constant-maximum aperture zooms "fixed aperture", and if they're not talking about mirror lenses you can usually assume that they don't actually mean it.
constant maximum aperture zoom lens - Lets say the lens is a 2.8f constant aperture and focal length is variable from 35mm - 100mm. It simply means that at 30mm through 100mm the 2.8f is available to use. Many variable lens say 3.5 - 5.6f meaning 3.5f at the 35mm focal and decreases towards 5.6 as the lens is zoomed out towards 100mm. So at 100mm fully zoomed out the largest aperture available to use is 5.6 . All this means is you need more light at the longer end of the lens. So a 3.5 constant can shoot in lower light than a 3.5-5.6 lens can.
There are two types of lenses in general - one with a fixed focal length, like 35mm, 50mm, 85mm or they have variable focal length range, like 18-55, 24-70, 70-200 etc.
Now when the focal length is fixed, those lenses are called prime lens, and lenses with variable focal length are called zoom lens.
Now when the focal length goes more than 85, they are termed as tele lens. So there could be tele prime lens, or tele zoom lens. And sometime you will find super telephoto lens, like 500mm and upward.
Now the shorter the focal length, the wider the lens is. In general, 24mm to 35mm is considered as wide lens, and anything that falls below 24mm are considered "ultra wide angle" lens.
And usually 8mm to 10mm lenses are considered as fish eye lens.
There are lenses specialized for taking snapshot of small objects and to magnify it extensively, those are known as macro lenses. You will find macro lenses with a specific mark as "macro" on lens body - like 60mm macro, 100mm macro etc.
Hope it helps.