Robert Browning’s poem “The Patriot” is a dramatic monologue where the speaker narrates his own story. He gives a detail account of how people celebrated and cheered fro him one year ago and how he is being led away now to be put to death. 
 
The poem has mainly been a depiction of the short public memory and fickleness of praise and glory. And the readers cannot be sure as to exactly why people celebrated one year ago. Maybe it was a victory in war or the assemblage for fighting one, or winning a popular election to an office, or being nominated as a ruler, or maybe something else. For that matter, we are also not sure who the speaker actually is, or why he is sentenced to death. 
 
This is only in the title of the poem that we find the word ‘patriot’. So, we can assume that the speaker was a patriot, at least in his own estimation. There are some clues in his own expressions —

Nought man could do, have I left undone;
And you see my harvest, what I reap

The speaker emphasizes that he has done no wrong. Rather he is misjudged and wrongly punished for his good deeds. 
 
Again, in the very last line of the poem, he says —

‘Tis God shall repay: I am safer so.

The speaker, sticks to his stand that he has done everything good for the people, so God will reward him in the heaven. He is a true patriot in his own assessment.
 
And, I guess, the poet too tried to show the man as a real patriot. Only then, the theme of the poem, the fickleness of public sentiment and morality, would be emboldened. From that angle, the title of the poem “The Patriot” is justified.