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Personal income climbed a moderate 0.6 percent in May and spending remained strong, the Commerce Department said Tuesday. ''We are clearly in a transitional phase,'' says Steven Wood, senior economist at Chase Econometrics. ''The more modest growth in personal income will be translated into more modest growth in GNP.'' Fears of the economic expansion coming to an abrupt end are premature, he adds. The fairly solid growth in personal income indicates economic expansion will continue through '84 .

The government's broad measure of income and spending showed major improvements in wages and salaries and an acceleration in the purchase of heavy duty items such as appliances and autos. Personal income, before taxes, grew to to $2.415 trillion, slowing from an April jump of 1.6 percent.

The personal income report provides the last major data necessary for the government to prepare its ''flash'' projection of how fast the economy has been growing in the second quarter.