With the lack of such usual along-the-way political stopping points as a county board or a state legislature in this city-state, it's no wonder that people are already lining up to replace Marion Barry and Arrington Dixon on the D.C. City Council, and also no wonder that most of the names are familiar.

Barry, the Democratic nominee for mayor, and Dixon, the sole candidate for City Council chairman, must win the Nov. 7 general election before their seats will be vacated. But that's not stopping would-be successors.

Barry's possible departure from the council offers two choice political plums. The first is his at-large council seat, which will be temporarily filled by the D.C. Democratic State Committee until an election can be held to choose someone to serve the remaining two years.

Secondly, if Barry is elected mayor there will be a vacancy in the prestigious, high-visibility post he used as a springboard to higher office - the chairmanship of the council finance and revenue committee, which frames most of the city's politically important tax legislation.

Barry's use of the finance committee post to advance his political career was in some respects ironic, for originally, the former activist had considered opting for the chairmanship of the council housing committee. Robert B. Washington Jr., now chairman of the D.C. Democratic State Committee and a lawyer who has made a big name for himself in business and political circles, convinced Barry otherwise.

Barry did such a good job of broadening his political base that he beat: Robert Washington's candidate, City Council Chairman Sterling Tucker, in the Sept. 12 Democratic primary. Now, other council members have taken note and are tussling for the inside track in the contest to become the next finance committee chairman.

The two most active seekers of the post, according to city hall sources, are David A. Clarke, the Democrat from Ward 1 who is virtually assured of reelection Nov. 7, and school board member Betty Ann Kane, the party's nominee for an at-large council seat, who is also considered an almost certain winner in next month's election.

Kane is stressing her previous work as chairman of the school board finance committee, while Clarke is quick to point out that he has served on the finance committee in the past, and, he claims, sponsored more tax legislation than anyone on the council except Barry.

It will be up to the council members to select the chairman of each committee once the new council session begins Jan. 2. The newly elected council chairman - probably Dixon - will undoubtedly have a key role in the choice.

Two of the four persons whose names are most often mentioned as possible candidates for Barry's seat have passed this way before. One is realtor H.R. Crawford, who lost to Kane in the primary. The other is maverick Democrat Douglas E. Moore, who lost to Dixon in the primary. Moore already holds an at-large seat, but his terms expires Jan. 2.

Two other names are familiar ones in a different way. One of these is Conrad P. Smith, the president of the D.C. School Board. The other is John Ray, the unsuccessful, come-from-nowhere candidate for mayor, who dropped out of the race a few weeks before the primary, endorsed Barry and subsequently won high praise from members of the Barry organization for his work on their candidate's behalf.

The possible candidates for Dixon's seat, representing the affluent Ward 4 in Upper Northwest, also include some leftovers from last month's primary: community activist Goldie C. Johnson and Robert V. Brown, both of whom lost the at-large race won by Kane, and Dorothy Maultsby, who ran for mayor for several months before throwing her support behind Mayor Walter E. Washington's unsuccessful bid.

Ward 4 regulars say that Victoria Street, who replaced Hilda Mason on the school board when Mason was elected to the council in 1977, is also interested in the seat.

Both of the new names have ties to Sterling Tucker. One is Andrew Coleman, a Howard University administrator, while the other is Charlene Drew Jarvis, a research psychologist at the National Institutes of Health. Both were active in Tucker's mayoral campaign.

The two top people in Mayor Walter E. Washington's campaign organization have returned to their jobs in city government. Lacy C. Streeter, the campaign manager, is back at work as the mayor's general assistant, while Warren Graves, the campaign director of field operations, has returned to his post as a special assistant to the mayor.

Both quit their posts to work for Washington and were reinstated to their old jobs last week. City Personnel Director George R. Harrod said city civil service regulations allowed both men to be rehired without competition because they were qualified for the jobs they had previously held and neither of the posts had been permanently filled in their temporary absence.