Yes, if the adoption’s failure was “finalized” in 2015, then you should amend your 2015 return (or else you can’t claim the 2014 expenses).
“A domestic adoption is the adoption of a U.S. child (an eligible child who is a citizen or resident of the U.S. or its possessions before the adoption effort begins). Qualified adoption expenses paid before the year the adoption becomes final are allowable as a credit for the tax year following the year of payment (even if the adoption is never finalized and even if an eligible child was never identified).”
Please see IRS Tax Topic 607.- https://www.irs.gov/taxtopics/tc607.html. Especially look at Example 4 under “Timing rules: For what tax year can you claim the credit?”
NOTE that foreign adoptions have different timing rules than domestic adoptions.
In terms of the baby’s lack of name and SSN, follow these IRS instructions to complete the input screen for the adoption credit.
"If you cannot give complete information about an eligible child you tried to adopt in 2015 because the adoption was either unsuccessful or was not final by the end of 2016, complete the entries that you can on line 1. Leave blank any entries you are unable to complete. For example, if you do not have an SSN or ATIN for your eligible child, leave column (f) blank." This is from the instructions for Line 1 on page 3 in the Instructions for Form 8839 (click here).
So don’t worry about entering the name of the child and the SSN/ATIN, just complete the rest of the input screen with the information you have.
Since you have to paper file (print and mail) an amended return, the lack of name and SSN will not cause a problem, although you should add a statement giving the summary of the adoption.
As for taking the expense for the trip to see the mother, this is useable for the credit –
“Qualified adoption expenses
For both the credit and the exclusion, qualified adoption expenses, defined in section 23(d)(1) of the Code, include:
- Reasonable and necessary adoption fees,
- Court costs and attorney fees,
- Traveling expenses (including amounts spent for meals and lodging while away from home), and
- Other expenses that are directly related to and for the principal purpose of the legal adoption of an eligible child. “ (from the Tax Topic 607 link above).