If I may make things slightly more complicated. As we know from Daniel 9:26-27, it is “the prince of the people who shall come” that confirms a covenant for 1 week (7 years). “The prince” in Hebrew is “nagiyd”. I believe this could be the “False Prophet”.

Elsewhere in the book of Daniel, the Anti-Christ figure is referred to as “king” which in Hebrew is “melek” such as in this verse;
Daniel 11:36 “And the king shall do according to his will; and he shall exalt himself, and magnify himself above every god, and shall speak marvellous things against the God of gods, and shall prosper till the indignation be accomplished: for that that is determined shall be done”.

So I’d suggest Daniel could have used 2 different titles to differentiate between these 2 different figures that seem to function as a tag team of sorts from what we see in Revelation 13.