Is Abe a first name or a last name?

Abe is both: a family name in some places and a given name in others. It is mostly a family name in Japan; mostly a given name in the United States.

How to address someone called Abe

Japan. Abe is a family name and is usually written first. Write Dear Mr. Abe or Dear Ms. Abe, or use the full name if you cannot tell which title fits.
United States. Abe is a given name. Hi Abe on first-name terms; formally, Mr. or Ms. goes with the family name, not with Abe.

Not sure which part of a full name is which? Check the full name with the country where the person is based.

People recorded in Wikidata who carry Abe as a family name or as a given name, by country of citizenship (749 in total).

Country	As family name	As given name	Family name share
Japan	587	0	100%
United States	1	81	1%
Canada	1	13	7%
Netherlands	0	14	0%
New Zealand	0	7	0%
Australia	0	7	0%
United Kingdom	1	5	17%
Germany	2	2	50%
Poland	1	2	33%
South Africa	0	3	0%

Wikidata covers notable people, so counts show how the name is used, not how many people carry it.

As a surname: about 2,938 people in the 2010 census, rank 10,837 among US surnames.
As a first name: 2,768 babies born between 1950 and 2017, 0% of them girls.

More on this naming tradition: How Japanese names work.