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I am sorry to hear about this situation. First of all, understand that it is not a good idea to begin a new company while the divorce is pending for two reasons:
1) She can potentially claim interest in the new company if it is created during the marriage before the divorce is finalized, and
2) Until the court formally divides the old company, or declares it yours (or whatever the Court decides), it is not clear who owns what part of the old company and thus who controls the name. If she receives majority of the company (by claiming she never abandoned it, for example), then she can revive the company possibly and then argue that she has intellectual property rights to the name.
Therefore, it is best to wait until the divorce is finalized.
But having said that, if the old company is dissolved for good, then there should be no issue starting another one with that name except LLC instead of Inc since the LLC is dissolved, will not be revived, and there is no possibility of the old company pursing the new company for the name.
However, if the old company is controlled by her, then technically, she can attempt to claim that the name belongs to her, and that the new company would be diluting the name by using the same name but simply Inc instead of LLC. If so, then this can get back into court on an intellectual property matter.
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