need help, american english difference

Hi, can soemone please identify the following:

Consider the word 'lodge'. Sometimes Americans will say it like 'lowdge', other times they will say it like 'laahdge' , with a pure 'a' sound rather than 'o'. Can someone tell me what areas it is pronounced like this and does this feature have a name?

Thank you

It's pronounced with an /a/ as in "father."

or like Roger, as in, Roger Lodge

Skip do you say lodger and larger the same?

Lodger and father have the same vowel sound as in "clock" for those of us who are low back mergers. "Larger" however has an R in it and being a rhotic speaker, I would pronounce the R in "farther" making the vowel sound completely different from "father" or "clock"

No, I pronounce the /r\/ in "larger." I'm from Texas, so I pronounce pretty much every written "r."