What should I use? I want to say we give the name xx-prog to the program (that I already described.
[...] and we name the program with xx-prog.
[...] and we name the program xx-prog.
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There is no need for a preposition there, though stylistically you may want to indicate that xx-prog is a name but putting it in quotation marks or italicising it. Name is a ditransitive verb, and the objects are the program and xx-prog.
Just like if you were naming a person. Or a ship.
I name this ship Endeavour, and may God bless all who sail in her.
We named our son Lucy.