How do the Seventh Day Adventist interpret the father's seal in Revelation 7:3?

Yes, Ellen G White declared that those who are sealed by God are Sabbath keepers – that is to say, those who follow the Mosaic Law and keep Saturday as the Sabbath. From the following quotations, please bear in mind that in the writings of Ellen G White “Sabbath” refers to Saturday, and “sabbath” refers to Christians who worship God on Sunday.

The following extracts come from this source: https://sdarm.org/publications/good-way-series/sealing-message-0

The early Adventists expected Christ to come very soon. And He could have come in the days of the pioneers (GC 458). In this case, the faithful believers who received the seal of God would have been the last generation of Christians - those that stayed alive and remained unto the coming of the Lord (1 Thess. 4:15). The number of God's subjects would have been completed in a short time. And Christ would have come. It was in this context that E. G. White wrote about the sealing work of Revelation 7:1-4 as a present event.

With regard to the 144,000 in Revelation chapters 4 and 14, those who have received the seal of God on their foreheads, it becomes clear that E.G. White believed they were Seventh Day Adventists who keep the Saturday Sabbath. The seal is the name of the Father written on their foreheads:

The numbered group referred to in Revelation 7:1-4 is the same group that is mentioned in Revelation 14:1-5, and again in Revelation 14:12, 13, where those among this group who happen to die before the coming of the Lord, are declared "blessed," because they still retain the seal, the "Father's name written in their foreheads," and still belong to the same group. [Written 1907]

As he [John] looked with intense interest he beheld the company of God's commandment-keeping people. They had upon their foreheads the seal of the living God, and he said: [Revelation 14:12, 13 quoted]. 6T 15.

Let us strive with all the power that God has given us to be among the hundred and forty-for thousand. 7BC 970.

As the result of the threefold message it is announced, 'Here are they that keep the commandments of God, and the faith of Jesus.' GC 453, 454.

In this context, the “us” are Seventh Day Adventists who uphold the Saturday Sabbath.

The above link explains in Section IV that the SDA Reform Movement holds to the original interpretation of E.G. White with regard to Revelation 7:1-4:

In conclusion, we abide by the original SDA teaching about the sealing work of Revelation 7:1-4, which, in our thinking, is in perfect harmony with the Bible and the writings of E. G. White.

In the issue of the great contest two parties are developed: those who 'worship the beast and his image,' and receive his mark, and those who receive 'the seal of the living God,' who have the 'Father's name written in their foreheads.' 7BC 980.

While we’re at it, the SDA book, ‘The Great Controversy’ published by Advent Books, and which contains original text by E.G. White, has this to say about the Sabbath, the Beast and the Image of the Beast:

Chapter 25 God’s Law Immutable: “In order to be prepared for the judgment, it is necessary that men should keep the law of God” (p. 267); “The Sabbath therefore lies at the very foundation of divine worship” (p. 268); the beast (Revelation 13:16-17) is the papacy (who break God’s commands). The image of the beast is apostate Protestantism who follow the Sunday worship. (p. 273); the mark of the beast is acceptance of allegiance to Rome (keeping Sunday worship) (p. 276).

Chapter 27 Modern Revivals: “The Sabbath was changed by the papal power” (p. 277).

Chapter 38 The Final Warning: “The Sabbath will be the great test of loyalty, for it is the point of truth especially controverted... While one class, by accepting the sign of submission to earthly powers, receive the mark of the beast, the other choosing the token of allegiance to divine authority, receive the seal of God.” [Revelation 73]

Chapter 40 God’s People Delivered: “The enemies of God’s law... see that the Sabbath of the fourth commandment is the seal of the living God... And when the blessing is pronounced on those who have honoured God by keeping His Sabbath holy, there is a mighty shout of victory.” (p. 395)

From all of the above it becomes clear that Ellen G. White believed only Sabbath keeping Seventh Day Adventists would receive the seal of God on their foreheads, and this seal is the Father’s name. Only they make up the 144,000.

You ask, “How to understand this interpretation”? Well, given that her expectations about the sealing of the 144,000 failed to materialise by the time of her death, and that resulted in a revised interpretation, all I can say is she was wrong and we should not place our faith in the interpretations of men or women. This reminds me of another denomination (active during the same time as E.G. White) who have also had to change their interpretations after events proved them wrong.