Another name for a political cartoonist

Caricaturist fits and may be the word you're thinking of:

caricaturist

a person who creates caricatures (= humorous drawings or descriptions that make someone's most noticeable features even more noticeable)

• A caricaturist will turn a person’s potato nose or jug ears into the dominant feature in the portrait.

• She had to contend with aggressive newspaper caricaturists who made the most of her hairstyles.

[CED]

Satirist also fits, but less closely as it is broader, a hypernym.

Satire is defined by Cambridge Dictionary:

satire [noun] [C or U]

a way of criticizing people or ideas in a humorous way, especially in order to make a political point, or a piece of writing that uses this style:

• political satire
• Her play was a biting/cruel satire on life in the 80s.

And an example given under 'satirist' (one who writes / performs / [draws ...] satirical pieces):

• Caricaturists and satirists appealed to their patrons, mocking the stylish servant, the well-dressed sailor, the respectable shopkeeper.

[the final example from the Cambridge English Corpus].

A political satirist might be called a lampoonist or lampooner. Lexico has

lampoon
_VERB

Publicly criticize (someone or something) by using ridicule, irony, or sarcasm.

Punch, the satirical magazine that lampooned the establishment for more than 150 years, has closed.