No one really did conquering - they would take land, take slaves,
... that's what conquest is.
But Vikings were Vikings, even if they occupy a settlement, the people of the settlement do not become Vikings
... only because the Vikings were typically small numbers of warriors? And post-Roman, for that matter.
When Rome conquered a place, they’d levy most of the men into the legion, and when they finished their service they became Roman
That's... not how it works.
First, the Legions were for citizens only. Non-citizens were not permitted to enlist.
Second, the Auxiliaries, what you're probably thinking of, were partly conscripted, but mostly volunteer, and very selective about their recruits. In no reality would they have taken most of the men of a region.
Third, the process of Romanization was gradual and largely unenforced - the Romans did not care if the native provincials became Romans or kept their native culture. The Romans, in fact, held a worldview wherein other peoples were better at certain things than the Romans, and that this was a good thing, because it meant Rome could organize their superior efforts for the greater good of the Republic.
Fourth, most regions after Roman conquest retained a great deal of self-government, as the Romans did not want the trouble of overturning local practices, unless they interfered with something like collecting taxes.
Fifth, Roman conquest was rarely so simple as "The Romans have conquered this place now" - there were often many graduations of Roman control which regions went through, and few regions had the same journey. The moment of conquest you're imagining, where the Legions march through after putting the enemy's armies and leaders to the sword, is not very common.
Sixth, the process of ethnic cleansing and assimilation are both widely attested to in the pre-Roman world, by peoples much more brutal about it than the Romans.