What is the technical name for the birth and death dates that follow a person's name?

I don't know if there is a standardized technical term for it, but if I had to talk about the concept or if I had to propose easily understood terms, I'd go with lifetime or life span. After all, the terms work fine in general usage.

Halley's comet was visible to the naked eye just once during Albert Einstein's lifetime, 1879–1955.

If you are talking about the year, month or season then it should be: Born in.

Example: I was born in 1980 (May, summer).

If you are talking about day of the week or a holiday then it should be Born on.

Example: I was born on Monday (Christmas day).

And about death:

• Die in: Used to denote the situation at the time of death.

Example: She died in peace.

• Die on: Used to denote the date of death.

Example: He died on 5 July this year.

In the art world, the artwork caption labels known as tombstones have what are formally known as "life dates." You can also find the term "life dates" applied descriptively in genealogy, biographical, encyclopedic, and other archival contexts.

Here's an excerpt from the Association of Art Editors style guide:

Life dates: Give in full. Examples:

       1908–1972
       Arminius (c. 17 B.C.–A.D. 21)
       385–331 B.C. (All digits are given for all B.C. dates.)

Abbreviations may be used in text for life dates given in parentheses. Examples:

       born = b. (b. 1930) Note: this is preferable to the form (1930–)
       died = d. (d. 1538)
       about = c. or ca. (ca. 1489–d. 1538)
       flourished = fl. (fl. 1503–30) (fl. 1530s) (fl. 16th century)
       date known but unverified = ? (1489?–d. 1538)
       active = act. (or spell out) (act. 16th century or active 1711–16)

Rutgers Art Review's editorial style guide calls them, quite literally, "parenthetical life dates":

As an aid to the reader, please provide parenthetical life dates for historical figures, as well as publication dates for works discussed in the main text.