Everywhere Faith Ryan Whittlesey of Pennsylvania goes this spring she encounters the name, image and presence of her opponent's father - former governor William Scranton.

"I'm boxed in," she complains. "I can't attack the father. He's revered in the state."

But at the same time she and the other GOP candidates for lieutneant governor clearly resent the candidacy political novice whose father's name is his chief political credential. "My father never made more than $100 a week in his life," she tells audiences. "I came up the same way you did: up from the rough and tumble, up by the bootstraps."

Her problem is a common one this year. Ballots all over the country carry the names of the offspring of prominient national political figures, seeking office on their own this year.

There's Brown in California, a Freeman in Minnesota, a Stennis in Mississippi, a Landon in Kansas, and O'Neill in Massachusetts, a Smathers in Florida, a Hodges in North Carolina, a Simpson in Wyoming and a Clement in Tennessee.

Some of them are incumbents with wee-established political reputations of their own. But a goodly number are running for office for the first time.

Nancy Landon Kasselbaum, for example, is running for the Republican Senate nomination in Kansas as "a new voice with a trusted name."

Her father is Alf Landon, the former Kansas governor and 1936 Republican presidential nominee.

A 45-year-old mother of four, she admits she wouldn't be running for the Senate if it weren't for her father's name.

"Name recognition is the name of the game in a crowded primary like we have this year (there are seven Republican candidates)," says one of her aides. "Alf Landon is a name people recognize in Kansas. It carries a very positive image."

A name can also carry liabilities. "There's always some resentment that government shouldn't be a family affair," says Mile Freeman, a candidate for Congress from a suburban Minneapolis district. His father, Orville Freeman, was popular governor and secretary of agriculture in the Kennedy-Johnson administration.

The liability is especially great this year in Minnesota. The Democratic-Farmer-Labor Party is showing signs of becoming a party of "the sons of." The state treasurer is James Lord, the son of a prominent former state attorney general and federal district judge. The state auditor is Jim Mattson, the son of another former attorney general. And until last Friday, Hubert H. Humphrey III, the son of the late senator and vice president, was a DFL candidate for state attorney general.

Freeman, making his first race for public office, decided not to have his father campaign for him. But he says, "Did is my most trusted adviser" and important fund-raiser.

Freeman's Republican opponent, Rep. Bill Frenzel, is a four-term congressman. "If he weren't Orville's son, Mile would probably be practicing law quietly somewhere," he says. "Other than being an nice guy he hasn't a lot of experience. He hasn't penetrated into community affairs. He has no experience in the state legislature, the city council or in neighborhood activities. He has a big appetite and a lot of ability."

There's nothing particularly new about sons following their fathers into politics. It dates back from the colonial period, according to Stephen Hess, author of "America's Political Dynasties!" There have been some 700 families in which two or more members have served in Congress and they account for 1,700 of the 10,000 men and women who've been elected to Congress since 1774.

"Every time you look at the dynaties it seems to overwhelm you," he says. "The idea of a democracy having royal families grates on many people."

Hess, however, doesn't feel the nation has been ill-served by the sons of famous men. Seldom do they steal from th public till, he notes. They also tend to weed themselves out.

"A famous name seems to be good for one free election," he says. "Then the son has to prove himself."

It probably isn't surprising that sons of politicians go into politics. Sons of doctors, after all, become doctors; sons of plumbers become plumbers. Politicians often don't leave their children great wealth, but Hess notes they leave two priceless commodities: connections and a brand name.

Sons are relying on these two commodities all over the map this year.

Bob Clement, 32, whose father Frank G. Clement, was a popular Tennessee governor in the 1950s, is seeking the Democratic nomination for that office this year. Another son of a well-known Tennessee Democrat, Albert Gore, whose father served in the U.S. Senate, is now a congressman.

In Mississippi, one of the leading contenders for a congressional seat in the Jackson area is John Hampton Stennis. His father, john C. Stennis, has represented the state in the Senate since 1943. "You don't run into people in Mississippi who say 'I never heard of Sennis,'" says the younger Stennis, a 40-year-old state legislator.

A second Edmund G. Brown is running for reelection as governor of California. Massachusetts Lt. Gov. Thomas P. O'Neill III, whose father is speaker of the House of Representatives, is seeking reelection after toying with running for the Senate.

Luther Hodges, whose father was a North Carolina governor and Kennedy administration secretary of commerce, is the frontrunner for the Democratic nomination for the Senate in that state. Aim K. Simpson, is running for the GOP nomination for the Senate.

But the two candidates with the longest family ties are probably Senate Minority Leader Howard H. Baker Jr. (R. Tenn.) and acting Mayland Gov. Blair Lee.

Both Baker's father and stepmother represented Tennessee in Congress, and his father-in-law was the late senator Everett Dirkson (R. III.). Lee is the 21st member of his family to hold elective office since a Lee entered the Virginia House of Burgesses in 1647.

The best father and son story of the year may belong to Florida Secretary of State Bruce Smathers, who is running for governor of that state. His father, George A. Smathers, a senator for three terms, checked into a Jacksonville hotellast month.