I think the answer is
Building.
Named after my creation
A building comes about as a result of building.
By ones in need,
Building society. (OP addition: Shelter is a basic human need.)
or ones of station
Master builders. (OP addition: Some buildings are built as status symbols; a station is a type of building.)
With bowing bays I wind and light
I think this refers to bow windows and bay windows found on some buildings to provide more light.
With barreling wagons I leap to a height
I think this refers to a barrel vault (also called a wagon vault) found in some buildings and usually forms part of the roof or ceiling. (OP addition: "Leap" is another word for "vault", if used as a verb.)
Though I cannot fly, my wings do protect
Buildings can have wings which, among other functions, can provide shorter escape routes in safety-critical buildings.
Through passing ages I paths correct
This refers to road building to create paths which has been done throughout the ages. (OP addition: Also, passing ages → passages i.e. corridors guide people through buildings.)
Mess up my plans and pay a terrible cost
Mess up the plans for a building and it could prove very costly.
Make me confused and all will be lost
I think confused here is a synonym for "unlisted" and unlisted buildings are not protected against demolition. (OP note: It's easy to get lost in confusing buildings.)
I'm in impossible dreams of tomorrow's Rome
"Rome wasn't built in a day" (OP note: Also, impossible dreams are "building castles in the sky")
I'm in Jesus shunning sand when placing a home
This refers to the Parable of Wise and Foolish Builders
I'm in trucks
Building trucks (OP note: and "built like a truck")
and tanks that were made to stay
I think this refers to things like water tanks found in many buildings. (OP note: or "built like a tank")
In one of my senses, or so they might say
Building site (sounds like 'sight') (OP note: Also, alluding to how the previous parts of the paragraph are sayings or idioms, all using the "to build" sense of the word.)
Yet does the gate to my name allow ingress?
Possibly a reference to the Red Gate Building which at one point house the Ministry of Transport Construction. (OP note: "Yett", "gate" and "ingress" are all words for entranceways.)
What am I—process, result, and progress?
Building is a verb and a noun referring to a structure and also the action of constructing something. (OP note: As well as the progress of something e.g. "the building suspense".)
