Final answer:
The Republican Party, rebranded as the National Union Party during the 1864 election, chose Andrew Johnson as Abraham Lincoln's running mate.
Step-by-step explanation:
During the presidential campaign of 1864, the Republican Party, in an effort to appeal to a broader set of voters, renamed itself the National Union Party.
In this process, they nominated incumbent President Abraham Lincoln for re-election and chose Andrew Johnson, a War Democrat from Tennessee, as his running mate for Vice President. This strategic partnership was aimed at unifying different political factions to support the Union during the Civil War and to promote a moderate approach for post-war Reconstruction.