Bank of Virginia Co. of Richmond yesterday completed its takeover of Union Trust Bancorp of Baltimore in the first merger of institutions from Virginia and Maryland since the two states approved reciprocal banking legislation last year.

The merger of the two bank companies will create a multibank holding company with assets in excess of $7 billion and with more than 220 offices in Maryland and Virginia. The two companies reported combined deposits of more than $5 billion immediately before the merger was completed.

It is the second interstate merger to be completed by a Virginia bank holding company in less than a week. United Virginia Bankshares, Inc. (UVB) of Richmond, the state's second-largest, took over the District's NS&T Bankshares Inc. last Friday for the first merger of D.C. and Virginia banking firms under the new interstate banking laws.

A merger agreement between Bank of Virginia Co. and Security National Corp. of the District is expected to be completed by the middle of the year, Bank of Virginia officials said yesterday. That merger would complete Bank of Virginia's "crescent strategy" for the Baltimore-Washington-Richmond-Tidewater region, officials added.

Bank of Virginia Co., the state's fourth-largest bank holding company, will continue to operate from its headquarters in Richmond, which is also the base of its principal subsidiary, Bank of Virginia. Union Trust Bank will continue to operate under that name in Maryland as a subsidiary of Bank of Virginia Co.

Under the merger agreement, which shareholders of both companies approved in November, each share of Union Trust's common stock will be exchanged for 2.05 shares of Bank of Virginia stock. Union Trust shareholders will receive instructions for handling the exchange in mid-January, officials said.

At least six other interstate mergers involving banks in the Virginia-Washington-Maryland region are expected to be completed in 1986. In addition to the pending merger between Bank of Virginia Co. and Security National, the following combinations are expected to be approved and completed this year: Sovran Financial Corp. of Norfolk, with D.C. National BanCorp Inc. and Suburban Bancorp of Bethesda; UVB with Bethesda Bancorporation; Dominion Bankshares Corp. of Roanoke with State National Bank of Rockville; James Madison Limited of the District with McLean Bank in Northern Virginia and First Continental Bank of Silver Spring.

The Sovran-D.C. National-Suburban merger would create one of the largest banking organizations in the mid-Atlantic region, with assets in excess of $12 billion. Sovran, with assets of nearly $9 billion, is the largest bank holding company in the Virginia-Maryland-D.C. region.