A.W. Clausen -- universally known as Tom Clausen to the banking fraternity -- will be taking over the presidency of the World Bank at a time that the borrowing needs of the poor nations that constitute its customers are multiplying fast and the funds to satisfy those needs have yet to be proffered by the rich nations.

In his valedictory speech to the World Bank-IMF Annual meeting four weeks ago, retiring President Robert S. McNamara called for a 50 percent increase in the bank's lending potential to meet the rising demand for loans, to finance major new energy development in the Third World and to take care of the banks's biggest and newest customer, China.

In an interview last night, Clausen spoke of the challenge he faces in keeping "the lesser-developed countries alive so we can effect long-term cures. . . .The next few years will be critical."

Clausen, the 57-year-old head of the Bank of America, will have to meet a stiff personal challenge: stepping into the shoes of a man who had won the plaudits of the Third World for an unbending commitment to the eradication of poverty and the alleviation of its bleak economic future.

But Clausen himself is well-known in many of the poor countries, an important factor -- as are his impeccable financial credentials -- in his nomination by President Carter. He is almost sure to bring a much different style to the job than did the emotional former Ford executive.

Clausen will have to take over an institution so uniquely dominated by McNamara over the past 10 years that it has become known as McNamara's Bank. Critics have said that McNamara surrounded himself with yes men and that the top executive layer at the bank is therefore weak. Others say it is McNamara who made the bank the powerful world force it is today.

Perhaps the most pressing problem facing the president-designate is that the U.S. Congress has proved reluctant to act speedily on appropriations for all international lending agencies. An official who himself had been on the "short list" of four final candidates said that "the major task for Clausen is to conduct the affairs of the bank so that Congress will be willing to appropriate the money. Then his major substantive challenge will be to continue McNamara's forward-looking and agressive approach."

As if it were not enough of a hassle to deal with a foot-dragging Congress, Clausen also will have to confront the insistent demand by the wealthy Arab nations for a higher profile in the bank.

If this demand is not met, the Arab group has made clear that it will be unwilling to provide additional funds -- notably for a new energy affiliate of the bank that McNamara proposed, following a suggestion of the Economic Summit meeting last summer in Venice.

The Carter administration, a strong supporter of McNamara and his general proposals to expand the bank's functions and lending power, has not yet committed itself to a new energy affiliate that would take over bank lending plans of some $13 billion for energy over the next five years and then double the program. Such an affiliate presumably could have Arab management at the top.

But the United States already has agreed to a general capital increase for the bank from $45 billion to $85 billion and to participate in a $12 billion restocking of funds for the bank's soft-loan affiliate, the International Development Agency. Pending congressional action -- potentially early in 1981 -- on the general capital increase, the Carter administration would like, for tactical reasons, to hold back on McNamara's proposal.

Treasury officials would like to get one capital increase through before having to shepherd a second one through Congress. But McNamara also brought up another way to expand the bank's lending potential, and that is by liberalizing the very conservative "gearing ratio" which limits bank loans, dollar-for-dollar, to the total of its subscribed capital and reserves.

In a recent Washington Post interview, McNamara said: "The time for the expansion of the . . .lending program is now." Yesterday, Clausen told The Washington Post that it makes good sense to explore the larger needs "before the problem becomes critcial. I think Bob McNamara is absolutely right in proposing ways to expand the funding of the World Bank."