switche company within US. i797 still valid, is stamping necessary.

USA H1B Visa
1 
Here is my case .

 

I was with company A with H1B stamped with validity till aug 2013 and I94 having same date.

I switched to company B with H1B validity till aug 2015 (NOTE : i did not travel outside, so stamping has not been done)  

-> I94 still has aug 2013 date

Now I switched to C  and H1B transfer receipt is valid till OCT 2013 ( no stamping still. because i was in US since company A)

->physical I94 still has same date  i.e aug 2013

 

 I want to know is it necessary to go for stamping if i travel in march 2013 even though my previous employer's visa validity date is aug 2013 . 

some people say company can ask bcoz they want their name on VISA.

 

Please advise.
2

When B and C’s petitions arrived, didn’t they have I-94s attached to the bottom of it?

IMO, it is not required to get visa stamped as long as the previous visa stamp is still valid. However, like others said, your employer can still ask you to go for stamping if they want their name on the visa stamp. When returning to US, you can show old unexpired visa stamp and latest 797 to gain entry to US and work for that employer.