Not true for me. My first exposure to Star Trek was the TOS Movies. I was taken to TFF at the age of 10 and it didn't convert me, but my parents showed me TVH a year later, which did hook me, and what was at the beginning of the VHS Tape? Everyone of a certain age knows this:it implies that its a lot closer in time period to the original, not 70-100 years later. It only seems like a good name now, because people got used to it.
A teaser for Star Trek: The Next Generation.
"The Next Generation" made the series sound cool. And that feeling didn't go away afterwards. In TVH, Kirk and crew were from the 23rd Century and their time looked better than our time. So, to my 11-year-old brain, I thought TNG being in the 24th Century and further in the future sounded even better.
Renting and watching "Encounter at Farpoint" scared me off from TNG initially, but I don't blame that on the title of the series.
Star Trek: The Fifth Generation would've sounded like a shitty title. And in fact, this stands out to me because I remember Peter David (RIP) being the person to mention this in an editorial at the top of the letters page in an issue of DC Comics Star Trek run, when they were talking about the 25th Anniversary. I remember that sticking out to me. And I agreed with him. He said The Next Generation, in his view, meant the next generation of fans and the next generation of there being TV series.