We can construct a table to find the possibilities. The information we know is:
Woman Dog Husband
Abigail George Frank
Bertha
Candy Jerry Horace
Dodi Frank
Eudora Ike
Also we know the Bertha's husband has the same name as George's dog.
First we note that the name Horace it's not in the Dog column, so the Bertha's dog is named Horace.
Woman Dog Husband
Abigail George Frank
Bertha Horace
Candy Jerry Horace
Dodi Frank
Eudora Ike
The Bertha' husband is named Ike becuase Frank and Horace are already used, and can not be George, so the posibilities are Jerry or Ike, but Jerry is the name of Horace's dog and the problem says the Bertha's husband has the same name as George's dog.
So, our table is:
Woman Dog Husband
Abigail George Frank
Bertha Horace Ike
Candy Jerry Horace
Dodi Frank Jerry
Eudora Ike George
The husband of Eudora is named George because his dog is named as Bertha's husband.
And this is the only valid result, because we construct the table with information provided and satisfying the constrains, in the process there was no other unambigous choices.