After reviewing accounts in the OR's, it appears this was an engagement between Wesley Merritt's Union Cavalry and Fitzhugh Lee's Cavalry and parts, at least of the divisions of B.R. Johnson, Henry Heth and George Pickett.

The "official" name according to the OR's is Tabernacle Church or Beaver Pond Creek. Both sides reported the engagement as a skirmish, with the Confederates using their artillery "freely".

Here is Wesley Merritt's Report from the OR's:

APRIL 4, 1865--4 p.m.
Brig.-Gen. FORSYTH, Chief of Staff:

GEN.: I have met the enemy in considerable force near Beaver Pond Creek. They seem to be inclined to hold the forks of the roads to Amelia Court-House and Goode's Bridge. (I have just received a report from Capt. Whiteford, with Mackenzie's division. I inclose it.) From all this there is no doubt about their holding Goode's and Bevill's Bridges, with a view of crossing the Appomattox. The force I sent on Bevill's Bridge road reports meeting the enemy. In how great a force I do not know. I will hold the forks at Tabernacle Church and find out what I can. Prisoners just taken report Heth, Johnson, and Pickett in our front with all the enemy's cavalry. They use their artillery freely. We have taken prisoners from Heth's and Johnson's divisions. The enemy does seem inclined to hold the roads, but not to advance. Prisoners just taken report that some said they were going to Amelia Court-House, and others across the Appomattox. Negroes report all trains gone to the bridges on Appomattox.

Very respectfully, your obedient servant,
W. MERRITT, Brevet Maj.-Gen.

and here is an excerpt from Bushrod Johnson's report:

"On Tuesday, the 4th of April, we moved at 8 a.m.; marched about four miles, in rear of Pickett's division, toward Amelia Court-House, to where the road by Tabernacle Church crosses the road to Court-House. The enemy appeared on the road to Tabernacle Church. A line of battle was formed across this road, and skirmishing, with artillery fire, on our part continued until night, the enemy's cavalry feeling my line from left to right. At night the cavalry formed to protect my right flank, and we rested until 3 a.m. on the 5th of April."

Both of these reports are found in:
CHAP. LVIII. THE APPOMATTOX CAMPAIGN.
[Series I. Vol. 46. Part I, Reports. Serial No. 95.]