Sen. Herman E. Talmadge (D-Ga.) acknowledged yesterday that his name appeared on a secret bank account here that a former Talmadge said was used to funnel improper Senate reimbursements to the senator and his family.

In a statement released by his official late yesterday, Talmadge, who is under investigation by the Senate Ethics Committee and a federal grand jury here, said he did not learn his name on the account until Thursday, when he was told by his administrative assistant and his attorney.

"Any signatures purporting to be mine on documents relating to the account were not affixed by me, authorized by me, or affixed with my knowledge or consent," Talmadge said.

In a June 13 memo the former aide, Daniel Minchew, said he put nearly $13,000 into the Riggs National Bank account after filing - at Talmadge's direction - two false expense claims with the Senate, one in 1973, the other in 1974. Minchew has also said that some of the money from the accounts went to Talmadge or to members of his family, but has declined to say whose name the account was in.

Sources say familiar with bank records said yesterday that as much as $40,000 was transferred through the account. The surces said the money came either from election campaign funds raised for the senator.

Talmadge has denied ever converting campaign contributions to his private use. A Talmadge aide declined yesterday to comment on the bank account beyond reading the senator's statement.

In July Talmadge turned over to Senate and Justice Department investigators a copy of Minchew's June 13 memo and records of two Senate reimbursements that went into the bank account. Spokesmen for Minchew have called the release of the Talmadge to make his former aide a "scapegoat."

Regarding the bank account, "Whatever was done was done with Sen. Talmadge's knowledge or consent or direction and on his behalf, " a Minchew attorney, Robert G. Fierer, said in a telephone interview from Atlanta yesterday.

Talmadge's name appears on several documents relating to the bank account, according to sources. But Talmadge and Minchew have both acknowledged that Minchew routinely used an automatic signature device to sign Talmadge's name to documents and checks.

Talmadge was questioned in his office for about 1 1/2 hours yesterday by investigators for the Senate Ethics Committee, Carl Eardley, the committee's special counsel for the Talmadge probe, said afterward that he would open "a full scale probe" into the Riggs bank account documents. Eardley said he was particularly interested in numerous deposits and withdrawals from the accounts.

During the questioning, Talmadge, who was with attorney James Hamilton, was never placed under oath and never refused to answer any of the investigator's questions, Eardley said.

But he declined to say whether he was satisfied with the 22-year Senate veteran's answer. "I'm satisfied in the sense that he was courteous and repsonsive," Eardly said. "He didn't offer me a cup of coffee."

The Senate committee is scheduled to question Minchew in late September, after the former Talmadge aide completes his grand jury testimony. Eardley said yesterday that he expects to return to Talmadge with more questions after the committee is through with Minchew.

Talmadge has already repaid about $37,000 to the Senate for other reimbursements he received between 1972 and 1977. He acknowledged that the money was paid to him for expenses that were either non-existent or not reimbursable, but said the vouchers for the funds were the result of mistakes by his staff.