Despite the name change IF the second marriage was bigamous to go through the procedure of a divorce was decidedly risky
The information and talk that would generally circulate about these matters would have stood a good chance of reaching wife No 1 who could have reported the matter to the police and thus his arrest. As said by others, at that time period a prison sentence was the normal outcome of any proceedings (if found guilty).
Given that he could afford financially to go through the Divorce proceedings against wife no 2 there is no evidence (so far) that he did not do the same with Wife No 1.
Absence of evidence is not proof to support a presumption of bigamy.