H1 reentry doubt

[vimau]

I just came to US on H1-B visa, but i am returning to India due to some personal reasons and is planning to come back after a month. Since i am leaving suddenly, my employer has extended the validity of offer letter till end of this year (31/Dec/2012).

Is there any problem in leaving the country within 1 week without joining the company which filed H1-B for me? Also in India I am planning to fix my passport by splitting my name (currently it doesn't contain a surname field) but whole name is in Given Name field.

[immihelp]

As long as the job still exists and the employer is willing to take you back, you can come back at any time within the validity of your LCA.