A woman these days is not required to adopt the husband's last name when they marry, though the marriage certificate is authority to do so. When a divorce occurs, barring some agreement to do so, she is not required to give up using the ex's name.
So yes, she can keep using Husband #1's name forever if she likes no matter how many times she's married or divorced. She's not compelled to change it. The only issue is that if she does start using a new name (like one of the subsequent husbands), it's likely to take a court order to go back to a previous one officially.