What i do is for example this:
After i created a busline in the town Beverley, i name that Beverley Bus. When i make a trainline i call it Beverley-London line. Or the other way around. This way i have them all sorted by name. I try to use the cityname where most lines will end up first. So in this example my main hub is Beverely. Same with cargo. In example i have 1 line hauling wood and brings it to the mill. I call that Woodline 1. Then the line from the mill to the city i call Products 1. With new lines i change the number to Woodline 2, Woodline 3 etc.
Edit: i missed your text where you asked if it was possible to rename then, yes you can. Click on the pencil when you are in line-building mode
Now, what you might have missed is that when you get a message of a bus or whatever that reached end of it’s live, click on that so a new window will open. On that new window you see a sort of dot on the top left corner. If you click on it it will centre the map to this vehicle. Now, check what line he drives, open your lines-window and press the Dollar sign on the right to send all vehicles to the depot and autosell them. In the meantime buy some new vehicles.
Note: That is what i do when i bought all vehicles of that line at the same time. If you later added newer cars to that line then it’s more of puzzle to find out which one is old and which one not. So i try to just buy around 10-12 vehicles at the same time, even when i just started out a new line, they will turn into profit pretty quick and in that way i can change them in 1 go.
One other note: It can be handy when you have the lines window opened to click on the Seeable Only (or whatever it’s called). This way when you hover over a city you will only see the lines that you can see on your map. When you get further in the game and have dozens of lines it makes it more clear what you are looking at.
Edit: One more tip:
On the left side below in your screen you can click on vehicles, the window that opens you can sort on age of the vehicles. So i normally check that every 15 minutes or so to make sure i replace them when things run as they run. I always hate it when i build a new line to get pop ups about old vehicles.