"Do we know if the Moderna and Pfizer vaccines change the DNA to allow body to be inmmune?  Or do we need another annual shot?"

The Moderna and Pfizer mRNA-based vaccines do not change the cell's DNA. They simply provide the mRNA blueprint to be translated (into the encoded spike protein) by the cells that take up the mRNA vaccine. The adenoviral based vaccines by Astrazeneca/Oxford and Johnson&Johsnon/Janssen also encode the spike protein and are not reported to change the host cell DNA.

Moderna, Pfizer, and Astrazeneca are 2 dose series spaced out by 4-12 weeks; the J&J is being tested as both a single or 2 dose series (57 day interval) and whether it will be approved for single dose or double dose is yet to be determined. The duration of immunity after receiving the intial vaccine series is yet to be determined. Most likely a booster vaccine injection will be needed. However, whether the booster is every year, every 2 years or some other interval is yet to be determined. 

BDAZ