Instead BNP candidates in Swansea East, Swansea West and Gower will appear as "Support Our Troops Bring Them Home".
The BNP said they had not intended just to use that name, but Swansea council said it was the party's decision.
The Electoral Commission said candidates can use a different name under the regulations.
It confirmed the move was legal, as the alternative name is a properly registered description for the BNP.
Voters will be able to tell that the three are official BNP candidates only from the party logo on the ballot paper.
Misled
A spokesperson for the commission said: "Our advice to voters is always to scrutinise the ballot paper very carefully."
A BNP spokesperson confirmed all three candidates are standing for the party, and not as a splinter group.
The spokesperson said a Swansea council official misled them when they filled in the candidate forms, which was why he said the three candidates were registered under the "Support Our Troops Bring Them Home" name.
He also said the forms used by the council were more complicated than those used by most other UK local authorities.
In response, the council said: "It was the BNP representative's decision to take [to put Support Our Troops Bring Them Home on the ballot paper] and he was in no way misled by Swansea council."
The council also said nomination papers filled out by the BNP were in a standard form produced for use across the UK.
"There is no material difference between the form used by the BNP and one produced by the Electoral Commission," it added.
BBC News
