Not at all, because the Enterprise-D is the fifth Federation starship to bear the name. NX-01 and the Ringship Enterprise were pre-Federation vessels. It's just simply a case of referring to things since the founding of the Federation.
This isn't always specified in the dialog though.
Actually it was.
In TNG's "Relics," when Scotty asked to see a holodeck recreation of the
Enterprise, the ship's computer wanted to know which one and specifically said:
"There have been five Federation starships with that name."
Scotty didn't specify he was looking for a
Federation starship. The computer simply assumed that because in its Siri-like database it recognized that this was a fairly common request, especially on a ship named Enterprise. It clearly didn't list the ringship or NX-01 despite those being logical possibilities in the phrasing of Scotty's actual request:
"The Enterprise. Show me the bridge of the Enterprise you chattering piece of..."
The computer didn't tell him "There have been 18 naval vessels, two spacecraft, three United Earth starships and five Federation starships with that name." It didn't tell him "There have been 26 vehicles with bridges that have that name." It specified "Federation starships" on the assumption that Scotty, like everyone else, wanted to see the bridge of one of the -D's predecessors. And what, prey tell, would the computer have done if Scotty had actually wanted to see NX-01?
Similar thing happens in the Temporal Investigations meeting. Sisko calls it "The First Enterprise" and nobody specifies whether he's talking about Federation starships or even spacecraft in general. For all they know, he could have answered the question with "It wasn't even a starship, it was the old CV-6 at the battle of Leyte Gulf." Here too the statement "There have been five" refers only to the major vessels everyone knows about because they get so much publicity. NX-01 gets no recognition at all, and neither probably would whatever puny nothing-vessel filled the gap between the -C and the -D (kinda like SP-790 USS Enterprise never shows up in the history mosaics or how nobody seems to be aware that there were five different sailing vessels all with the same name, none of which were exactly alike).
Not necessarily. Retiring the ship and moving it to a museum was probably enough of an honor.
Naming a starship after his first command is a relatively small gesture by comparison. They'd actually have to have a coherent reason NOT to use that name in order to deliberately skip over it.
And for several decades, when most people thought of the Enterprise, they thought of NX-01 and none other.
Exactly. They'd have been crazy NOT to assign the name to one of NX-01's successors, if nothing else to appeal to public nostalgia for those early days of discovery. The only reason NOT to use the name is if the Enterprise did something embarrassing or controversial during its brief Federation service, something the public would prefer not to be reminded of every time somebody mentioned its name.
There's the slim possibility, of course, that they simply changed conventions and started naming exploration vessels after, say, mountains or famous scientists (e.g. USS Kelvin) but even in that case it's unlikely the name Enterprise wasn't simply relegated to a non-exploratory vessel whose class didn't follow the same naming conventions.
It's also worth pointing out that the Abramsverse -- which Enterprise is arguably an integral part -- has at least one other Enterprise before NCC-1701.