Was there a plan "B" for the D-Day?

technically, D-day WAS plan B. The invasion plans called for the invasion to happen on 5 June, not 6 June, but were postponed because of bad weather.
Had it failed that day (I think the 7th was also an option), a wait of at least a month was have been called for to get the correct conditions again, and that was considered to be too long to remain operational security, effectively meaning there'd be no invasion in Normandy, would be too risky.

Had that happened, other things would have to be designed. Maybe Calais after all, or cross the North Sea and land in the Netherlands. Or break out from Italy and southern France and strike north from there.
Things would certainly have gone a lot different, and probably a lot more bloody.

But theorising on that borders on alternative history fiction, which is well outside the scope of this site.

The most likely Plan B would have been to amp up Operation Anvil/Dragoon, the invasion of the south of France, possibly moving it forward from its actual date of August 15, 1944. With a lodgement made there, a subsequent cross channel invasion could be tried as soon as feasible.

There were a range of contingency plans in addition to the full-scale invasion plan OVERLORD that were prepared for possible Allied return to the continent in 1944.

You can read about them here:-
HISTORY OF COSSAC (CHIEF OF STAFF TO SUPREME ALLIED COMMANDER)

They included the RANKIN plans, CASE 'A', CASE 'B', and CASE 'C', which provided for a return to the continent under varying degrees of German military or political disintegration;

RANKIN 'A' allowed for a return under conditions of weakened German resistance.
RANKIN 'B' allowed for a return after German withdrawal from the occupied countries.
RANKIN 'C' allowed for a return after surrender or complete collapse of German power.

There were also feigned decoy operations planned against Norway ('TINDALL'), the Pas de Calais ('STARKEY'), and the French west coast ('WADHAM') which might have been developed further in the event of a failure of OVERLORD.

With the Soviet steamroller steaming towards and perhaps beyond Berlin it is very likely one or more of these plans might have become operative as alternatives or in conjunction with the planned invasion of southern France ('DRAGOON').

At an operational level there were too many unknowns in advance of the actual landing to have concrete alternative plans.

However on D-Day morning itself the planners were working furiously on various means of dealing with the debacle on Omaha. Options being considered by Bradley were a withdrawal from Omaha, either alone or coincident with a withdrawal from Utah, to consolidate on the British beaches (Gold-Juno-Sword). Montgomery was looking at ways to possibly divert V Corps reinforcements for Omaha through Gold Beach. (Montgomery - Master of the Battlefield page 623 by Nigel Hamilton)

In the event, the original plan for Omaha was modified as (A General's Life by Omar Bradley, page 251)

Twelve destroyers moved in close to the beach, heedless of shallow water, mines, enemy fire and other obstacles, to give us close support. The main batteries of these gallant ships became our only artillery. Huebner's chief of staff, Stanhope B. Mason, later wrote: "I am now firmly convinced that our supporting naval fire got us in; that without that gunfire we positively could not have crossed the beaches."
...
Privately, I considered evacuating the beachhead [of Omaha] and diverting the follow-u troops to Utah Beach or the British beaches.

and (ibid, page 256) the original plan for Collins' VII Corps was adjusted:

Early on the morning of June 7 ... Monty and I decided to secure a link-up of V Corps [Omaha] and VII Corps {Utah] at Carentan as quickly as possible and at the same time a link-up of U. S. and British Forces.

(The original plan had called for VII Corps in its entirety to swing west across the Cotentin peninsula to cut off and capture Cherbourg, with V Corps protecting its flank - now part of VII Corps had instead to be diverted to protect V Corps.)

Update:
Note hat in general military operations don't have any Plan B; instead there are reserves allocated which will be used to bolster units which encounter difficulties, and to take advantage of opportunities that present themselves. The idea is to spread the attrition amongst your own troops as evenly as possible, and attempt to concentrate it against particular units of the enemy, so that the enemy runs out of reserves before you do. At this point the enemy's line breaks and a victory is imminent, if reserves are still in hand with which to grasp it.

Eisenhower had written a speech should the landings have failed.

Our landings have failed and I have withdrawn the troops. My decision to attack at this time and place was based on the best information available. The troops, the air and the Navy did all that bravery could do. If any blame or fault attaches to the attempt it is mine alone.

Stephen Ambrose in his essay "D Day Fails" in What If? states "there was no alternative plan available". He supposes Operation Dragoon would have gone forward and been reinforced with extra troops, but would not have proven decisive.

When Operation Overlord began, the Allies had already been fighting in Italy for some time; Rome was taken on June 4th, 1944, two days before D-Day. Thus, "plan B" was already ongoing. Invasion of southern France was also planned, and it happened on August 15th.

From a global strategic point of view, Germany was already losing on the Eastern front; in June 1944 they were retreating. Stalingrad was in the past, the siege of Leningrad had been lifted, Ukraine had already been regained by USSR. It was rather clear that the Soviets would reach Berlin, as long as part of Germany's army was kept occupied in the West. For that, the threat of an invasion was enough. If D-Day had failed, Germany would still have lost the war. The main strategic goal of USA, at that point, had shifted: since Germany's defeat was more or less ensured, the biggest priority had become to prevent the Soviets from expanding their influence zone over Western Europe.

If D-Day had failed, Allied forces would still have beaten Italy, then entered southern France. However, the USA/UK position at Yalta would have been weaker, and one can imagine that the resulting post-War European landscape would have been different; plausibly, the whole of Germany, and Austria and Denmark as well, would have been integrated into the "Eastern Block".