First time travel to US on a visa which has different name than I 797

[aspirantal]

Currently I am in India and a company A from the US applied H1B for me and I got visa stamped.
Even before I traveled to the US, company B wanted me in their company and applied H1B and I got it approved.
so, I have visa on the name of A and the approvals of both A and B.
I have decided to join B and will have to travel shortly to US.
I have asked my lawyer and he said I should be able to travel to US with the visa on the name of A and the original petition of B.
i have two questions here.

Can I really do that?
If so, what should I tell the immigration officer at the POE if he/she were to ask me about why I didnt go for another visa interview on the name of company B?

Any quick help is greatly appreciated.

Thanking in advance

[immihelp]

You can do that.

You don't really have to join company A, if you don't want to.

Legally, there is no need to get another stamping as long as the previous stamping has not expired.