No, you retain your original alignment.
Not only does the spell itself not mention your alignment changing to match the creature you turn into, but comparing it to the Polymorph line of spells seems to imply that it has no effect on your alignment.
Looking at the Greater Polymorph description:
If the form is that of a dragon, the spell functions as Form of the Dragon I.
So we can infer that the spells are functionally the same, with the exception that Form of the Dragon only permits you to turn into dragons. Polymorph and Greater Polymorph similarly do not mention alignment at all. However, if we look at Baleful Polymorph:
If the spell succeeds, the subject must also make a Will save. If this second save fails, the creature loses its extraordinary, supernatural, and spell-like abilities, loses its ability to cast spells (if it had the ability), and gains the alignment, special abilities, and Intelligence, Wisdom, and Charisma scores of its new form in place of its own.
This shows that Baleful Polymorph explicitly does not change the target's alignment unless specific conditions are met--and if the more malicious version of Polymorph can only do so conditionally, there's no reason why Polymorph or Form of the Dragon, intended to be cast on self or allies and able to be dismissed at will, would have any impact on the target's alignment.
Nature of Alignment
Even aside from the implication of similar spells, the alignment listings for creatures aren't meant to be descriptive of every example of that species. They are meant to be templates for the average specimen. This leaves room for GMs to subvert player expectations with civilized orcs, fallen celestials, and the like. When you cast a Polymorph-like spell, you're turning into a version of that creature with your memories, your personality, and your moral values.
Having Polymorph-like spells change alignment would make them fairly restrictive--casters would be limited to creatures with alignments similar enough to their own (and motivations and desires which do not conflict with theirs) that their transformed "self" could be guaranteed to not sabotage the intended goals they had before transforming. This would be an interesting idea for an in-universe rule of magic, but as stated above, the RAW do not seem to support it being the default.