How does 一个， 一位，一名 change the meaning of a sentence?
In English, an article such as "a", "an", "the" is essential element before a countable noun. In Chinese it is optional.

Comparing "He is a teacher" with "他是老師". 他/He implies there is one person. "a" is redundant.

In "他是一位老師" and "他是一名老師",  "一位" and "一名" is a kind of respect to a teacher. 位 means position and rank. 名 means famed.  In the old days, Chinese showed their high respect to teachers.

"一個" is a common measuring word. Saying "他是一個老師" is like treating a teacher as a common object or a common person. 

In practical, 一 is redundant and people often say "他是位老師" and "他是名老師". So do "他是個老師".

In Classical Chinese, we can writing "他是一老師" if we emphasize it it "one".