Backed by the might of the Syrian government and its 30,000 soldiers here, Lebanese President Elias Sarkis today named his own man to head the army, his first public definance of diehard Christian rightist forces.

He acted after the Tiger militia of Christian warlord Camille Chamoun, a former president, called for a general strike and blockaded streets in the Christian section of Beirut to protest the firing of Gen. Hanna Said as army commander.

Before dawn today, a bomb destroyed part of Foreign Defense Minister Fuad Butrost apartment, but Butros and his wife escaped unhurt. Police said the blast was caused by about 20 pounds of dynamite.

Naming a new army commander is the strongest step Sarkis has taken since September, when he became president, toward declaring his indenpendence from Christian rightists toward declaring his independence from Christian rightists and toward rebuilding Lebanon's army to the point that it can take over from the Syrian dominated Arab peace-keeping force that ended 19 months of civil war.

For years Chamoun has dominated the selection of army officers, most of whom are his supporters.When it became clear last week that Sarkis was firm on replacing Said, 54, Chamoun submitted names of three other supporters for the post and threatened to escalate the fighting in southern Lebanon if one of his men were not chosen.

Instead, Sarkis reached down in the ranks to pick Col. Victor Khoury, 48, a former armored and intelligence officer favored by the Syrians. Khoury was promoted to general.

It was obvious that the Syrian government, which has been urging Sarkis to move quickly to rebuild the army, stood behind his actions. This morning Syrian troops moved quickly to remove the barricades erected by the Tiger militia, and editorials in two Syrian newspaper today attacked Chamoun for obstructing the effort to rebuild the Lebanese army, fractured during the civil war.

Khoury, who sat out the civil war without taking sides, now must try to reconcile factions of the army that were fighting one another as recently as last fall.

During the war, the army split into at least four groups: those who fought for the Christian rightists; the Lebanese Arab Army, which backed the Moslem leftists; those who supported Syria and remained neutral in their bases; and those who went home and did nothing.

The split was so great that the air force was never used because Christian pilots feared that Moslem mechanics would sabotage the planes if they were used against leftist or Palestinian forces.

The army of 7,000 is now totally Christian and works out of a headquarters in a Christian suburb of Beirut. It is top-heavy with officers and has few young fighters. Most of the men wear combat fatigues, but they are usually tucked into expensive soft-leather boots.

The Moslem leaders of the Lebanese Arab Army have been taken to Syria, and other Moslem soliders are afriad to travel through Christian territory to the army headquarters.

Although Khoury - like Said and most other officers - is a Maronite Christian, his appointment was hailed today by Moslem politicans. Said was considered to have been too close to rightist Christians during the civil war.

The appointment also was supported by the Phalangist party, signaling a sharp split within the ranks of the Christians. The Phalangist, party, which supplied the bulk of rightist forces during the civil war, also opposed the Chamoun party's strike call today "a negative act."