Tamir is not just Tall. The name Tamir means - upright, tall, loud, high class. The word Tamir expresses uprightness and exaltation in the physical and spiritual sense and is attributed to a set of qualities of nobility and to a person with unique virtues. Hence, parents who call their son this are wishing him to be able to face the difficulties he will face and move forward.
There is also a different name that is pronounced the same and written the same in English, but differently in Hebrew - טמיר (beginning with tet instead of tav.) This name means "secret, hidden" (from a word usually used in religious context to describe a most holy secret or mystery.)