Tufts Medical Center has tapped Eric J. Beyer, an insider who built up its doctors group over the past five years, to be CEO of the 415-bed Boston hospital. Beyer, 50, will take the reins Oct. 1, the start of the hospital’s fiscal year. He succeeds CEO, Ellen M. Zane, 60, who will retire at the end of September. The appointment assures continuity at the city’s oldest hospital. Beyer has worked closely with Zane, who has been widely credited with leading a financial turnaround at Tufts. The hospital was losing more than $18 million when she arrived in 2004 but posted a profit of $5.3 million last year, according to state figures released earlier this month. But like other hospitals in Boston and across the state, Tufts will face intense pressures in the coming years as the state and federal governments reduce payments for Medicaid and Medicare, health insurance programs that cover low-income and older patients. Those programs account for slightly more than half of the Tufts payer mix.