If I am offered food and I am not sure if it's halal. Can I bless it in Allah's name to make it permissible?
If it is haram (wine, pork, carrion, dedicated to idols etc.) it can not be made halal.
He has only forbidden to you dead animals, blood, the flesh of swine, and that which has been dedicated to other than Allah . But whoever is forced [by necessity], neither desiring [it] nor transgressing [its limit], there is no sin upon him. Indeed, Allah is Forgiving and Merciful.
Allah forbade from eating these items, He did not tell to just say His name before eating. Really, if your inquiry was possible then there was no point of Allah telling us what is haram and what is halal, He ought to have just told us to always say His name before eating everything.
Maybe you are confused because of the hadith: https://sunnah.com/bukhari/97/27. This hadith is irrelevant as that meat was halal since it was prepared by Muslims, the only concern was that they might have not known to say Allah's name while slaughtering. This hadith only proves that omitting Tasmiyya by a Muslim butcher because of forgetfulness or ignorance does not make the meat haram.
Come on brothers, Islam has been made very easy for us. We should try our best to avoid (potentially) haram foods. Nowadays, halal foods are available everywhere.
When you have doubt in your mind if the food is haram, it is best to avoid it. You can surely wait a while and eat halal food afterwards. Making the food permissible by blessing it with Allah's name is a trick used by most of us because of our impatience, negligence and greediness.
You should only eat halal food as ordered by Allah:
“Eat not (O believers) of that (meat) on which Allah’s Name has not been pronounced (at the time of the slaughtering of the animal)”
And He says concerning haram things (interpretation of the meaning):
“He has forbidden you only the Maytah (dead animals), and blood, and the flesh of swine, and that which is slaughtered as a sacrifice for others than Allah (or has been slaughtered for idols, on which Allah’s Name has not been mentioned while slaughtering)”
In the name of Allah
In regard to your inquiry concerning halal rule, apparently it can be counted as a halal food in it is cooked or made in an Islamic food as general rule which it should be done in Islamic rule. (I said it as the viewpoint of Shia school of though. Although I assume the viewpoint of Sunni school of thought can be like this as well. But in non-Islamic countries, you cannot be optimistic regarding the issue, since as a rule, logically in non-Islamic countries they do not scarified the animals based on Islamic rule...
Meanwhile it is true that reciting or saying Allah's names is so good, but every thing has its specific rules and we ought to them according to Islamic rules as have mentioned.