No. It should reflect intended retirement year, not age.
From Vanguard's website:
The year in the fund name refers to the approximate year (the target date) when an investor in the fund would retire and leave the workforce.
A lot of retirement planning advice has a built-in assumption that everybody plans to retire when they are approximate 65 years old, give or take a couple years. Sounds like this advisor is working off that assumption, and refusing to consider alternate retirement timelines.
These funds start out more aggressively/riskily invested, primarily in stocks with few if any bonds, leading to higher volatility but more potential for growth. As retirement nears and you want to use it as a source of income, the portfolio shifts to a more stable and less risky allocation in order to preserve capital. If you invest in the fund that targets the year you turn 65, and then you retire at 40, your portfolio's allocation may not (likely won't) fit your risk tolerance.