It depends on the specific lens design. Many telephoto zoom lenses keep roughly the same minimum focus distance throughout the zoom range, but not all do.

Manufacturers often publish just one minimum focus distance for a zoom lens, usually because that figure is most relevant at the longest focal length, where maximum magnification is also typically highest. For most zooms, both the minimum focus distance and maximum magnification are most important at the telephoto end.

So the listed 1 m is often a practical spec for the lens as a whole, but the exact behavior across the zoom range can vary by model. If you need to know precisely whether it changes at different focal lengths, check that lens’s detailed manual or test it directly.