If I limit myself to …
1. "Old name"
2. New company
… I can identify three directions a such sequel can take.
Real sequel
Still Life 2, Monkey Island 5 (episodes), Gothic 3: Forsaken Gods, Eye of the beholder III, Max Payne III, Simon the Sorcerer 4 etc
The real sequels that practically take the same characters, gameplay and continue the story of the former titles. It is rare to see that sort of sequel when many years have passed between the former and the later game. This direction can usually be taken when the former games were left in a cliffhanger. When the final game had a very satisfying ending you have to ask if the sequel is actually needed. A bit off-topic but let it be known; I DO NOT WANT BALDUR'S GATE III so stop asking for it you idiots out there, someone might actually hear you!
The new Story
Arcania, Fallout: Tactics, Fallout 3, Fallout: New Vegas, the new Larry titles, Red Faction II, Silent Hill: The Room, Silent Hill 5, Baldur's Gate: Dark Alliance
The sequels that keeps the theme of the old game and you can easily see that it is much inspired of the old ones, but often use a new location (but keeps the setting, sometimes moved ahead or back in time), a new main character, a different story. I find this an acceptable use of the name. They of course exploit the brand, but they can be done with respect to the former titles. They tend to be a bit more pushed though. Usually slapping a number in the title is a problem, which was much discussed over Fallout 3 that wasn't a sequel to F2 but a standalone game.
Fallout: Tactics is difficult to place in my 3 categories. It's actually not completely canon, it was made by another company, but it's still close enough when it comes to gameplay.
Baldur's Gate: Dark Alliance is not really a sequel, but a standalone series that even got it's own sequel. Baldur's Gate is a city and the plot is still in Forgotten Realms, so it fits the "other story" concept.
WTF
Might & Magic, Ultima, X-Com, Far Cry 2, Alone in the Dark: New Nightmare, Alone in the Dark: Inferno, TUROK, Golden Axe: Beast Rider, Bard's Tale, Fallout: Brotherhood of Steel
The truly distasteful habit that much be pointed out here, are the ones who is entirely different than the former titles. Different character, different world, sometimes completely different gameplay, different everything. Usually they are so different that reviewers tend to point this out in the first sentences of the reviews and ask why the name is used or what happened with the old characters that are nowhere to be seen.
Fallout: Brotherhood is neither a sequel, neither canon, neither follow the same gameplay as previous titles.
TUROK and Bard's Tale are cases of taking an old title, throwing everything out then keeping some basic themes from the old ones but with almost no relation whatsoever to older titles.
The most common question in the first sentences of every review for Far Cry 2 was "Where is Jack Carver" or "Gone is the tropical islands".
Alone in the Dark: New Nightmare, aka "four", is at least called "new". It's not set in the same era as former titles, the character is named Edward Carnby, but at least the title seems to point things out.
Alone in the Dark: Inferno, aka "five", did have a character named Edward Carnby. Why he is in 2010 and not the early 1900 like in earlier games, is actually explained, however, he is younger, much larger build (biker-style), use foul language, lost his moustache, was no longer an academic, and the worst part is that the universe no longer was the Cthulhu mythos but had now gone into Judeo-Christian mythos.
Let's not talk about X-Com.
The curious case of Silent Hill
Silent Hill is actually an interesting case. SH5 was actually made by a new company, but all "sequels" in SH are standalone, so it could have fit into the "true sequel" as well. However, SH4 "The Room" was originally made as a different story and was renamed "Silent Hill" later in it's production. This wasn't questioned by fans since it was very easy to make it so it fit the old series, thanks to the "each sequel is it's own story" concept of it's prequels.
