In short, yes.
In some rare cases, religious pursuits for the wrong reasons are viewed by the Gemara as "poisonous" -- Tosfos explains, if you're only studying just so you can get back at someone, that's no good.
But generally, we say "let a person engage in Torah and mitzvahs [there are varying texts whether it's 'Torah', 'Torah and mitzvahs', etc.] for ulterior motives, as it will bring him to the right motives."
Similarly the Gemara says a person who gives a hefty sum of tzedaka in the hope that the merit will save a deathly-ill relative is an "absolutely righteous person", so long as they don't explicitly regret the donation if the relative doesn't pull through.
The practice of noting donors is a well-established one, and if you search the Gemara you'll find parts of the Second Temple that had been dedicated by donors. Shulchan Aruch describes the practice too, as have twentieth-century responsa. (Rabbi Moshe Feinstein got some of these; as did Rabbi Eliezer Waldenberg in Israel -- I recall one where an old, widowed rebbetzin donated a new Torah cover, and asked that her name be embroidered on it. The yeshiva receiving it felt it was inappropriate to have a woman's name on it -- Rabbi Waldenberg told them, in short, go jump in a lake.)
As for costs -- it's the institution's choice how to spend the money, and if they think a plaque is in their best interest, then by all means. A charity is allowed to have some overhead. (By oral tradition from Rabbi Yaakov Kaminetsky, in theory overhead can be up to 49%).
From a US legal perspective, as I understand it, if the benefit is purely a ritual one (such as a high holiday seat -- which wouldn't be worth anything if you weren't a member of that faith), then whatever you pay for it is a charitable donation. If you take out an ad in your synagogue's dinner journal, if you're promoting your business then that's business activity (both maaser and tax-wise, I think); if it's "mazel tov honorees and best wishes", that's charity as you're receiving very little dollarized benefit. (Yes, reputation, but that's amorphous.) Similarly a synagogue/school banquet seat usually costs, say, $100; if you ask they'll tell you the cost of your meal is maybe $40. So that's a $60 donation, both tax-wise and maaser-wise.
As usual, disclaimer -- this is not official tax advice, obviously.
