Three hundred and forty six (346) is represented in Hebrew as שמ״ו, which is literally His name.
Like with all names, they are not the actual being and essence (מהות ועצמות) of the one represented by the name. Yet, the name is intrinsically bound to that essence. In the language of Chassidut, Name is only intended as a kind of handle for another and that handle is the means for the other to grasp and to connect to the Essence associated with that name.
In traditional Torah related abbreviations, 346 (שמ״ו) is the abbreviation for Heavens and Earth (שמים וארץ).
And it is in this context that 346 teaches us many important principles in the Torah.
Bereshit 14:19
וַיְבָרְכֵהוּ וַיֹּאמַר בָּרוּךְ אַבְרָם לְאֵל עֶלְיוֹן קֹנֵה שָׁמַיִם וָאָרֶץ׃
We learn that the blessing of Malkitzedek, who was King of Shalem and Priest to G-d above, was that Avram was blessed to G-d above, owner of Heaven and Earth.
And this follows the teaching found in Mishlei 3:19
יְהוָה בְּחָכְמָה יָסַד־אָרֶץ כּוֹנֵן שָׁמַיִם בִּתְבוּנָה׃
That G-d founded the Earth with wisdom and established the Heavens with understanding. And through this process, they became His possession, like Rashi teaches.
And just as the blessings of Avram came from the Owner of Heaven and Earth, so too, this is the source of our blessings as found in Tehillim 115:15
בְּרוּכִים אַתֶּם לַיהוָה עֹשֵׂה שָׁמַיִם וָאָרֶץ׃
In addition to this referring to the One who blesses us, it also reminds us that G-d is the one who helps us, both individually, like in Tehillim 121:2,
עֶזְרִי מֵעִם יְהוָה עֹשֵׂה שָׁמַיִם וָאָרֶץ׃
and collectively, like in Tehillim 124:8.
עֶזְרֵנוּ בְּשֵׁם יְהוָה עֹשֵׂה שָׁמַיִם וָאָרֶץ׃
And it is taught from Midrash Mishlei 31:5 that if we are engaged in Torah day and night, G-d counts it for us as if we are partners with Him in maintaining Heaven and Earth.
אמר הקב"ה לישראל: בניי, היו מתעסקים בתורה ביום ובלילה, ומעלה אני עליכם
כאילו אתם מעמידין שמים וארץ, שנאמר (יהושע א ח): "לא ימוש ספר התורה הזה
מפיך והגית בו יומם ולילה"
And this same sentiment is repeated by the prophet Jeremiah 33:25.
כֹּה אָמַר יְהוָה אִם־לֹא בְרִיתִי יוֹמָם וָלָיְלָה חֻקּוֹת שָׁמַיִם וָאָרֶץ לֹא־שָׂמְתִּי׃
And 346, through this phrase Heavens and Earth, also reminds us of the final redemption like is referenced in Tehillim 134:3
יְבָרֶכְךָ֣ יְ֭הוָה מִצִּיּ֑וֹן עֹ֝שֵׂ֗ה שָׁמַ֥יִם וָאָֽרֶץ׃
And it also teaches us about the World to Come like in Isaiah 65:17.
כִּי־הִנְנִי בוֹרֵא שָׁמַיִם חֲדָשִׁים וָאָרֶץ חֲדָשָׁה וְלֹא תִזָּכַרְנָה הָרִאשֹׁנוֹת וְלֹא תַעֲלֶינָה עַל־לֵב׃
And all of this is directed toward the unification of Heaven and Earth to reveal His Oneness like is expressed by Ramban to Shemot 20:13:1.
שתי לוחות כנגד שמים וארץ וכנגד חתן וכלה וכנגד שני שושבינין וכנגד שני עולמים. וכל זה רמז אחד, והמשכיל יבין הסוד:
That just as the two tablets of the law are one, so too, Heaven and Earth are one, Bridegroom and Bride are one, Moshe and Aharon (the two Escorts) are one and this world and the World to Come are one.
And this sentiment is what was expressed by Zecharia 14:9.
וְהָיָ֧ה יְהוָ֛ה לְמֶ֖לֶךְ עַל־כָּל־הָאָ֑רֶץ בַּיּ֣וֹם הַה֗וּא יִהְיֶ֧ה יְהוָ֛ה אֶחָ֖ד וּשְׁמ֥וֹ אֶחָֽד׃
And the L-rd shall be king over all the earth; in that day the L-rd will be one and His name (שמ״ו) one.