Tottenham Court Road (TCR) station was there before Centre Point was even thought of. Warren Street is at the junction of that street and TCR - there is nothing wrong with the current name. Similarly Goodge Street station is at the junction of that street and TCR.
As you say the current entrance at Chancery Lane is a little away from that street. However changes in the entrance is not a great reason to rename stations. Hatton Garden would be wildly inappropriate - further than Chancery Lane and in actual fact Farringdon is closer to Hatton Garden.
There is absolutely nothing wrong with the name of Holborn.
Finally the Bakerloo at Charing Cross was originally called Trafalgar Square until Charing Cross was rebuilt for the Jubilee line in the 70s. There is absolutely zero reason to undo that.
en.m.wikipedia.org
Centre Point may be a fairly recent concoction, however St. Giles Circus goes back rather further. As you say, there's two other stations which debouch onto Tottenham Court Road (one of which used to be so named, and sits roughly at the mid-point of that thoroughfare rather than tucked away at the extreme south end). The TCR name may be appropriate for the Central Line, but IMO it's completely inappropriate for the Northern, hence why it's one I'd look at.
I find the Holborn name completely inappropriate. As well as the fact that the street named Holborn sits some considerable distance to the east, even further east than Chancery Lane station, the Holborn area is generally regarded to be bounded by what is now Holborn station and running eastwards to roughly the Farringdon Road. Chancery Lane station is far more strategically positioned to serve that area than today's Holborn, which more serves what would be regarded as Bloomsbury to the north, Aldwych to the south, and perhaps to a lesser extent St Giles and Covent Garden to the west. Like TCR which has arisen purely because of a quirk of history in terms of being a suitable name for the Central Line station which came first, we only have Holborn because it happened to be the nearest station on the Piccadilly Line, remembering that the Central Line didn’t have a station here until the 1930s. If things were being designed from scratch now I think it’s highly unlikely both these stations would be named as they are, and I’d say it’s a certainty Chancery Lane wouldn’t be.
As I said, Hatton Garden was a bit of a wild card, as Holborn is a more suitable name for Chancery Lane. The reason I gave Hatton Garden a mention is simply that Chancery Lane station is heavily used by people heading there. Farringdon doesn't get this to the same extent.
The renaming of Trafalgar Square to Charing Cross was all well and good when the Jubilee Line linked the two stations, however we now have a situation where the two sets of platforms are now some considerable distance apart, with pretty much separate street entrances. I don't find this particularly satisfactory, especially as it encourages tourists (virtually all of whom would be coming to visit Trafalgar Square, rather than Charing Cross) to arrive at the "wrong" part of the station.
