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No, there's no common name specifically for the remainder of a term that is picked up by the elected POTUS' Vice President.
It seems like it would be a useful thing to have a name for, particularly since 1951 when the passage of the 22nd Amendment made elected terms special in that you can't have more than two of them. However, a VP has only ascended to the Presidency twice since then, and it hasn't happened at all in over 40 years.
In the specific case of LBJ, he served out the remainder of JFK's term, and then was elected to a four year term on his own once. If he'd been able to run and win again, he would have ended up serving for a bit over 9 years. After that, he would have been constitutionally barred from running again.