So I was going to adopt a 3yr old dog from someone who can no longer care for her. I already have one dog currently. The problem... they both have the same name. How would I go about changing the new dogs name when my current dog has her old name?

I have changed the names of both my current and previous dogs, but they weren't living with another dog who would be called using the old name. I don't see a good solution. Maybe add a syllable to the 3 year old dog's name and hope for the best.

Is there a name that rhymes or is close to the name with consonants?

Gabby instead of Debbie? Fifi instead of Pepe? etc.

You would be surprised how fast they catch on to a new name. Think of shelter dogs, a lot of them are renamed by the staff and then renamed again by the new owners.
It's just like teaching a dog a command such as sit or stay.