Can I resubmit under my company an abandon patent that was under my name?

If I submitted a patent under my personal name and it was abandoned, can I later resubmit or rather submit it under my company name?

You would have some challenges.

First, one cannot revive an abandonded application without a lot of effort, and perhaps some luck. It typically involves filing one of two types of petitions. Whether it is even possible depends of the circumstances of abandonment. See 37 C.F.R. 1.137.

Second, if the abandoned application was published, then that publication may be cited as prior art against a subsequently submitted application, even by the same inventor.

Assigning the patent application to the comapny is relatively straightforward. Maybe you could focus on a patentably distinct improvement and file that application.

Good luck.