Usually at the end of the any rituals it is said as sarvam sree krishnaarpanam (all the outcomes belongs to Krishna - a crude translation) and Krishna name is chanted thrice or ten times.
Vaishnavites use a prayer called saathivk thyagam (sacrifice of all outcome of the efforts) in which it is said to offered to Baghavan and none in specific.
Why is that it is dedicated to Krishna and why not Rama etc. I mean is there any specific reason behind it?
Yes. We say śrī Kṛṣṇārpaṇamastu (श्री कृष्णार्पणमस्तु) at the end of almost every ritual. It means everything goes to śrī Kṛṣṇā.
Not only people whose ishta devata is Krishna say this but almost every Hindu says this.
Why only Krishna not Rama etc., ?
In the Bhagavad Gita, Krishna Paramatma says to Arjuna :
यत्-करोषि यद्-अश्नासि यज्-जुहोषि ददासि यत् |
यत्-तपस्यसि कौन्तेय तत्-कुरुष्व मद्-अर्पणम् || २७ ||yat-karoṣi yad-aśnāsi yaj-juhoṣi dadāsi yat |
yat-tapasyasi kaunteya tat-kuruṣva mad-arpaṇam || 9.27 ||Whatever you do, whatever you eat, whatever you offer in sacrifice, whatever you give away, whatever austerity you practice, O Kaunteya, do that as an offering to Me.
By this verse he assures that He will take the offering to the proper destination without any cuts and discounts. People who worship other deities(Shiva, Amba, etc.,) too say śrī Kṛṣṇārpaṇamastu for this reason.
Commentary of Bhagavad Ramanujacharya on above verse :
Whatsoever secular work you do for the maintenance of the body, whatsoever you set aside for the sustenance of the body, whatsoever religious rites, obligatory (nityam) and occasional (naimittikam) you practice, like offering oblations into the sacred fire, performing charity and austerity — do all these as an offering to Me. Arpaṇa means offering — do all acts, secular and religious, as if the doer, the enjoyer and the worshipped were all offerings to Me.
There are other verses too
कायेन वाचा मनसेन्द्रियैर्वा
बुद्ध्यात्मना वा प्रकृतेः स्वभावात् ।
करोमि यद्यत्सकलं परस्मै
नारायणायेति समर्पयामि ॥kāyena vācā manasendriyairvā
buddhyātmanā vā prakṛteḥ svabhāvāt ।
karomi yadyatsakalaṃ parasmai
nārāyaṇāyeti samarpayāmi ॥(Whatever I do) with my Body, Speech, Mind or Sense Organs,: (Whatever I do) using my Intellect, Feelings of Heart or (unconsciously) through the natural tendencies of my Mind, Whatever I do, I do all for others (i.e. without the sense of attachment to the results), (And) I Surrender them all at the Lotus Feet of Sreemannarayana.
If your destination is moksha, you should not possess any fruits of efforts you have done. puṇya takes you Swarga and pāpā takes you to hell. These too are are not considered moksha. SO if you want to gain the moksha the liberation, all your fruits of effort should be given to the supreme Lord.
That's the reason we offer our deeds saying śrī Kṛṣṇārpaṇamastu (श्री कृष्णार्पणमस्तु) or similar statement.
Krishna and rama are same but krishna is called purnavatar(full incarnation). Every thing and every partical of this universe is Krishna. Krishna is inside us we are within Krishna. One interesting thing you should know that Rama and krishna were exactly copy of each other except their eyes. राम कृष्णा दोउ एक हैं, अंतर नहीं निमेष। इनके नयन गंभीर हैं, उनके चपल विशेष।
Krsna.