They're not exactly verbalisations as the word is repeated silently.
The reason for it is that the function of meditation is to stop the monkey mind and by having the word as well as the breath to concentrate on it's somewhat easier to slow the thoughts.
I'm only guessing why the word "buddho" was chosen but my guess is that it's either Thai or Pali for buddha and it was a meditation technique taught to me by Thai forrest traditional monks.

Oh right 'Bhutto' in Thai is 'Buddha', apparently.

In the anapana it's not practical to move around because that makes the subtlty of feeling the breath more difficult, but in mindfulness, vipassana, insight, meditation they specify four poses: sitting, lying down, standing and walking. This is still best formally practiced in a seated position. There are 3 reasons why other postures are sensible. 1) When the seated position becomes too painful, then standing or walking for a little while helps to maintain continuous practice; 2) Lying down is because people practice in bed; and 3) it is a continuous practice, so walking eating washing up, writing posts - everything is mindfulness.